ICMA-V
The Fifth International Conference on Mathematical Modelling and
Analysis of Populations in Biological Systems
October 2-4, 2015
Hosted by
Department of Applied Mathematics
University of Western Ontario
In
London, Ontario, Canada
Organizing Committee:
Advisory Committee:
• Jim Cushing, University of Arizona
• Lindi Wahl, Appl. Math., UWO
• Jia Li, University of Alabama in Huntsville
• Pei Yu, Appl. Math., UWO
• Saber Elaydi, Trinity University
• Liana Zanette, Biology, UWO
• Linda Allen, Texas Tech University
• Xingfu Zou (Chair), Appl. Math., UWO
Sponsored by
2
ICMA-V
October 2-4, 2015
Table of Contents
Table of Contends
I. Schedule
3-8
II. Abstracts
I-1. Abstracts of Plenary talks
pp. 9-12
I-2. Abstracts of 30 minute talks
pp. 13-53
I-3. Abstracts of Posters
pp. 54-59
III. UWO campus map
pp. 60-61
IV. Participant list
pp. 62-64
Notes:
Abbreviations for the buildings appeared in the schedule (see the three ovals on the first campus map:)
MC—Middlesex College building;
PA—Physics and Astronomy building
SSC—Social Science Center building;
Registration will be available on Friday on site in SSC and MC buildings, outside the conference room
SSC 2036, and MC 204; and on Saturday in MC, outside the conference rooms MC 110.
Posters will be arranged on Saturday and Sunday in MC, outside the conference room MC110.
Parking information: Parking in the two hotels is free; for parking information on campus, see the
maps.
Session Chairs: To make life simple and easy, we decide to let the first speaker of each session to be chair
that session; if the first speaker cannot be there he/she can pass it to the second speaker. The main job of
a session chair is to control the time, so that all sessions can be synchronized
3
Friday October 2 —–Morning
8:30-8:55
Registration
8:40-8:55
Opening
8:55-9:55
Plenary talk in Room SSC 2036, Chair Jia Li:
Sebastian Schreiber —— Explosions, extinctions, and metastability
9:55-10:00
outside Room SSC 2036
in Room SSC 2036
Walk to the Graduate Club in the MC buidling
10:00-10:30
S1
10:30-11:00
11:00-11:30
11:30-12:00
12:00-12:30
S2
10:30-11:00
11:00-11:30
11:30-12:00
12:00-12:30
S3
10:30-11:00
11:00-11:30
11:30-12:00
12:00-12:30
12:30-1:30pm
Coffee Break: hallway outside MC204
Room MC 15A
Ben Bolker:
Optimal mutation rates for parasite exploitation in a seasonal epidemic model
Troy Day:
A PDE model for the evolution of epigeneticallly inherited drug resistance
David McLeod:
Pathogen evolution under host avoidance plasticity
Maia Martcheva:
On the principle for host evolution in host-pathogen interactions
Room MC 17
Elena Braverman:
Competitive spatially distributed population dynamics models:
does diversity in diffusion strategies promote coexistence?
Wenxian Shen:
Spreading speeds and traveling waves of two species competition systems
with nonlocal dispersal in periodic habitats
Andrew Nevai:
Population dynamics in a producer-scrounger patch model
Xiaoying Wang:
Modelling the fear effect in predator-prey interactions
Room MC 204
Fred Brauer:
Age of Infection Epidemic Models
Keng Deng:
Dynamics of an SIS epidemic reaction-diffusion model
Michael Li:
Turning Points and Relaxation Oscillation Cycles in Simple Epidemic Models
Karly Jacobsen:
A hybrid model for epidemics on a contact network using a pair approximation result
Lunch
4
Friday October 2 —–Afternoon
1:30-2:30
S4
2:40-3:10
3:10-3:40
3:40-4:10
S5
2:40-3:10
3:10-3:40
3:40-4:10
S6
2:40-3:10
3:10-3:40
3:40-4:10
4:10-4:40
S7
4:40-5:10
5:10-5:40
5:40-6:10
S8
4:40-5:10
5:10-5:40
5:40-6:10
S9
4:40-5:10
5:10-5:40
5:40-6:10
6:30–8:30
Plenart talk in Room SSC 2036, Chair Jim Cushing:
Hal Smith —— Mathematical modeling of bacteria and virus interactions in a chemostat, petri dish,
and in marine environments
Room MC 15A
Pauline van den Driessche:
Seasonal and Pandemic Influenza
Jacques Bélair:
A model for the propagation of malaria between two populations
Peng Yu:
Global dynamics of multi-group epidemic models with non-strongly connected transmission networks
Room MC 17
Jin Wang:
Calculating the basic reproduction numbers for non-homogeneous epidemic models
Jonathan Dushoff:
Initial growth rate, generation intervals and reproductive numbers in the spread of infectious disease
Daniel Munther:
A remark on the global dynamics of competitive systems on ordered Banach spaces
Room MC 204
Yuming Chen:
A delayed HIV-1 model with virus waning
Naveen K. Vaidya:
Modeling the Risk and Dynamics of HIV Infection under Conditions of Drugs of Abuse
Wenjing Zhang:
Mechanisms underlying the generation of disease recurrence
Coffee Break: hallway outside MC204
Room MC 15A
David Earn:
Patterns of plague in London over four centuries
Sharon Bewick:
La Crosse Virus Encephalitis: Understanding Disease Dynamics at the Interface
Between Epidemiology and Invasion Biology
Alison Wardlaw:
Virulence evolution of a parasite infecting male and female hosts
Room MC 17
Daniel Coombs:
Interpretation and modelling with super-resolution microscopy
Gerda de Vries:
A Model of Microtubule Organization in the Presence of Motor Proteins
Stèphanie Portet:
Modelling intermediate filaments
Room MC 204
Yuan Yuan:
Dynamics of an HIV virotherapy model with nonlinear incidence and two delays
Ashrafur Rahman:
CD4+ T cell count based HIV treatment: effect of initiation timing of ART on HIV epidemics
David W. Dick:
Determining viral load set point and time to reach viral load set point
among patients infected with HIV-1 subtypes A, C and D
Reception: In the atrium of the PA building .
5
Saturday October 3 —–Morning
9:00-10:00
10:00-10:30
S10
10:30-11:00
11:00-11:30
11:30-12:00
12:00-12:30
S11
10:30-11.00
11:00-11:30
11:30-12:00
12:00-12:30
S12
10:30-11:00
11:00-11:30
11:30-12:00
12:00-12:30
S13
10:30-11:00
11:00-11:30
11:30-12:00
12:00-12:30
12:30-1:30
Plenary talk in Room MC 110, Chair Linda Allen:
Natalia Komarova —— Calculus of Stem Cells
Coffee Break: in the first floor of MC, outside the conference rooms
Room MC 110
Sue Ann Campbell:
Conservative Plankton Models with Time Delay
Gergely Röst:
Dynamics of the two delays Bélair-Mackey equation and delayed recruitment
models with maximized lifespan
Xiaoqiang Zhao:
Basic Reproduction Ratios for Periodic Compartmental Models with Time Delay
Tibor Krisztin:
Periodic Solutions of a Differential Equation with a Queueing Delay
Room MC 105b
Timothy Reluga:
On the evolution of seasonal migration
Lin Wang:
Complex alternative stable states in a three dimensional intraguild predation model
Frithjof Lutscher:
Dispersal, stability, and synchrony in predator-prey metacommunities
Yijun Lou:
Stage-structured models of intra- and inter-specific competition within age classes
Room MC 17
Xiang-Sheng Wang:
Transmission dynamics of avian influenza
Martha Garlick:
Connecting Local Movement of Mule Deer with Regional Spread of Chronic Wasting Disease
Matt Betti:
Age Before Bee-auty: An Age-Structured Model of Honey Bees, Disease,
and Environmental Hazards
Alex Petric:
Mathematical modeling of honeybee populations, some of their diseases and other stressors
Room MC 204
Thomas Hillen:
Navigating the Flow: the Homing of Sea Turtles
Saber Elaydi
Hierarchical competition models with the Allee effect and immigration
Ross Cressman:
Evolutionary game theory under time constraint
Brian Ingalls:
Displacement of bacterial plasmids by engineered unilateral incompatibility
Lunch, provided in the Graduate Club, in the ground floor of MC
6
Saturday October 3 —–Afternoon
1:30-2:30
Lord Robert May award talk, in Room MC 110, Chair Saber Elaydi:
Gail Wolkowicz —— Optimizing biogas generation using anaerobic digestion
2:30-3:00
Coffee Break: in the first floor of MC, outside the conference rooms.
S14
3:00-3:30
3:30-4:00
4:00-4:30
S15
3:00-3:30
3:30-4:00
4:00-4:30
S16
3:00-3:30
3:30-4:00
4:00-4:30
4:30-4:45
S17
4:45-5:15
5:15-5:45
5:45-6:15
S18
4:45-5:15
5:15-5:45
5:45-6:15
S19
4:45-5:15
5:15-5:45
5:45-6:15
Room MC 110
Jane Heffernan:
Vaccination, Screening, Treatment and Bifurcations
Chang-Yuan Cheng:
Adaptive dispersal effect on the spread of a disease in a patchy environment
Scott W. Greenhalgh:
Human behaviour and infectious disease transmission: a hybrid system approach
Room MC 105B
Jessica M. Conway:
HIV Viral Rebound Following Therapy Suspension: Stochastic Model Predictions
Libin Rong:
Modeling HIV treatment and slow CD4+ T cell decline
Pooya Aavani:
The Role of CD4 T Cells in Immune System Activation and Viral Reproduction in a Model
for HIV Infection
Room MC 17
King-Yeung(Adrian) Lam:
A mutation-selection model for evolution of random dispersal
Matteo Smerlak:
Structure of fitness distributions in evolutionary dynamics
Yuanwei Qi:
Traveling Waves Solutions of Non-KPP Reaction-Diffusion Systems
Break
Room MC 110
Linda J. S. Allen:
Estimation of the Probability of Invasion and the Time to Invasion Failure in Markov Chain
Models Populations and Epidemics
Jennifer Reid:
The Fixation Probability of Budding Viruses with Applications to Influenza A Virus
Mahnaz Rabbani:
A Location-Based Model for a Newly Proposed Class of Mobile Genetic Elements in Prokaryotes:
Mobile Promoters
Room MC 105B
Chris Cosner:
The reduction principle, the ideal free distribution, and the evolution of dispersal strategies
Chai Molina:
Evolutionary stability in continuous nonlinear public goods games
Fei Xu:
Evolution of mobility in predator-prey systems
Room MC 17
Michael R. Kelly:
Prophylactic vaccination strategies for disease outbreaks on community networks
Robert Smith?:
The viral spread of a zombie media story
Michael Williamson:
Successional genetics of incipient ring species complexes: isolation by distance and adaptations
7
Sunday October 4 —–Morning
9:00-10:00
10:00-10:30
S20
10:30-11:00
11:00-11:30
11:30-12:00
12:00-12:30
S21
10:30-11:00
11:00-11:30
11:30-12:00
12:00-12:30
S22
10:30-11:00
11:00-11:30
11:30-12:00
12:00-12:30
12:30-1:30
Plenart talk in Room MC 110, Chair Lindi Wahl:
Michael Doebeli ——Diversification and long-term co-evolution in high-dimensional
phenotype spaces
Coffee Break: in the first floor of MC, outside the conference rooms.
Room MC 110
Jim M. Cushing:
On the dynamics of an evolutionary population dynamic model and life
history adaptations to climate change
Shandelle M. Henson:
Effects of Warming Seas: Cannibalism and Reproductive Synchrony in a Seabird Colony
Shigui Ruan:
Modeling the Geographic Spread of Rabies in China
Junping Shi:
Is Rotational Harvesting really good?
Room MC 105B
Jia Li:
Staged-structured models for interactive mosquitoes
David Champredon:
Generation Interval Distributions
Connell McCluskey:
An SEI Model with Immigration and Continuous Infection Age
Zsolt Vizi:
Pairwise model for non-Markovian SIR type epidemics on networks
Room MC 17
Gail S. K. Wolkowicz:
Sensitivity of the General Rosenzweig–MacArthur Model to the Mathematical Form
of the Functional Response: a Bifurcation Theory Approach
Rebecca C. Tyson:
How seasonally varying predation behaviour and climate shifts affect predator-prey cycles
Bingtuan Li:
Persistence and Spreading Speeds of Integro-difference Equations with A Shifting Habitat
Adèle Bourgeois:
Overcompensatory dynamics in IDEs
Lunch, provided in Graduate Club in the first floor of MC.
8
Sunday October 4 —–Afternoon
1:30-2:30
Plenary Talk in Room MC 110, Chair Pei Yu:
Jianhong Wu ——Treatment-Donation-Stockpile Dynamics In Convalescent Blood
Transfusion Therapy
2:30-3:00
Coffee Break: in the first floor of MC, outside the conference rooms.
S23
3:00-3:30
3:30-4:00
4:00-4:30
4:30-5:00
S24
3:00-3:30
3:30-4:00
4:00-4:30
4:30-5:00
S25
3:00-3:30
3:30-4:00
4:00-4:30
4:30-5:00
Room MC 110
Yasuhiro Takeuchi:
Mathematical Modelling and Analysis of Tumor-Immune Delayed System
Siv Sivaloganathan:
Glycolysis & other metabolic pathways in cancers
Mohammad Kohandel:
Modeling aspects of cancer stem cells
Ali Mahdipour-Shirayeh:
Plasticity and Cell Division Competition in Colorectal Cancer Development
Room MC 105B
Don Yu:
Temperature-driven model for the abundance of Culex mosquitoes
Matthew Badali:
An Extension of the Fisher-Wright Model with Longer Coexistence Times
Yixiang Wu:
Coexistence and competitive exclusion in an SIS model with standard incidence and diffusion
Alexandra Teslya:
Predator-prey models with distributed delay
Room MC 17
Hermann J. Eberl:
Cross-diffusion in multispecies biofilms
Qasim Ali:
Ecological benefits of CRISPR-CAS systems to bacterial colonies
in the presence of phage infection
Daniel A. Korytowski:
Persistence in Phage-Bacteria Communities with Nested and One-to-One
Infection Networks
Alina Nadeem:
Time Capsule Evolution: Recombination with Proviral DNA Promotes Viral Persistence
9
ICMA-V, October 2-4, 2015
Abstracts II-1——Plenary Talks
Diversification and long-term co-evolution in high-dimensional phenotype spaces
Michael Doebeli
Department of Zoology and the Department of Mathematics
University of British Columbia
E-mail:[email protected]
Adaptive dynamics is a general framework to study long-term evolutionary dynamics. It is typically
used to study evolutionary scenarios in low-dimensional phenotype spaces, such as the important phenomenon of evolutionary branching (adaptive diversification). I will briefly recall the basic theory of
evolutionary branching and review a well-studied empirical example. Because birth and death rates of
individuals are likely to be determined by many different phenotypic properties, it is important to consider evolutionary dynamics in high-dimensional phenotype spaces. I will describe some results about
evolutionary branching in high-dimensional phenotype spaces, as well as results about the existence of
non-equilibrium evolutionary dynamics, such as chaos. Finally, I will present new results about how the
nature of the (co-)evolutionary dynamics changes as diversity evolves in high-dimensional phenotype spaces.
This leads to some new perspectives on how micro-evolutionary processes can generate macro-evolutionary
patterns, such as diversity saturation and punctuated equilibrium.
Calculus of Stem Cells
Natalia Komorova
Department of Mathematics
University of California Irvine
E-mail:[email protected]
Stem cells are an important component of tissue architecture. Identifying the exact regulatory circuits
that can stably maintain tissue homeostasis (that is, approximately constant size) is critical for our basic
understanding of multicellular organisms. It is equally critical for figuring out how tumors circumvent
this regulation, thus providing targets for treatment. Despite great strides in the understanding of the
molecular components of stem-cell regulation, the overall mechanisms orchestrating tissue homeostasis are
still far from being understood. Typically, tissue contains the stem cells, transit amplifying cells, and
terminally differentiated cells. Each of these cell types can potentially secrete regulatory factors and/or
respond to factors secreted by other types. The feedback can be positive or negative in nature. This gives
rise to a bewildering array of possible mechanisms that drive tissue regulation. In this talk I describe a
novel stochastic method of studying stem cell lineage regulation, which is based on population dynamics
and ecological approaches. The method allows to identify possible numbers, types, and directions of control
loops that are compatible with stability, keep the variance low, and possess a certain degree of robustness.
I will also discuss evolutionary optimization and cancer-delaying role of stem cells.
10
ICMA-V, October 2-4, 2015
Abstracts II-1——Plenary Talks
Explosions, extinctions, and metastability
Sebastian Schreiber
Department of Evolution and Ecology
University of California, Davis
E-mail: [email protected]
Populations in nature consist of finite numbers of individuals and are at constant risk of extinction.
The dynamics of these populations are well-represented by Markov processes on countable state spaces.
For small, asexual populations, extinction risk is particularly acute and interactions among individuals
are rare. Branching processes provide a useful approximation for these dynamics and (generically) exhibit
a fundamental dichotomy: extinction in finite time or unbounded growth which is often interpreted as
population persistence or establishment. This unbounded growth only occurs with positive probability if
individuals on average replace themselves.
In contrast, for small, sexual populations, individuals must mate to reproduce and, consequently, exhibit
frequency-dependent interactions. Using mean limit ODEs, I will present results that determine whether
unbounded growth occurs with positive probability or not in frequency-dependent branching processes.
For large populations, interactions among individuals are common but extinction tends to be far into
the future. Consequently, Markov processes representing these dynamics often exhibit long-term persistent
behavior (”meta-stability”) before extinction occurs. Using large deviation theory and tools from dynamical
systems, I will show how this transient behavior is characterized by attractors of associated mean-limit
equations, and how the length of these transients scales with the ”size” of the system.
As time permits, I will illustrates these ideas with models of SARS outbreaks, evolutionary emergence of pathogens, establishment of invading sexual populations, and stochastic Lotka-Volterra models of
community dynamics.
[1 ] Faure, M., Schreiber, S.J., Quasi-stationary distributions for randomly perturbed dynamical systems,
Annals of Applied Probability. 24, pp. 553-598 (2014).
[2 ] Faure, M., Schreiber, S.J., Convergence of generalized urn models to non-equilibrium attractors,
Stochastic Processes and their Applications. 125, pp. 3053-3074 (2015).
11
ICMA-V, October 2-4, 2015
Abstracts II-1——Plenary Talks
Mathematical modeling of bacteria and virus interactions in a chemostat, petri dish, and in
marine enviroments
Hal L. Smith
School of Mathematics and Statistics Sciences
Arizona State University
E-mail: [email protected]
I will describe recent joint work with collaborators on the modeling of bacteria-virus interactions in
laboratory environments such as the chemostat and Petri dish, as well as in marine environments. In the
setting of the chemostat, we are concerned with sharp conditions for persistence versus extinction of the
virus in the classical mathematical models formulated by Levin, Stewart, and Chao (1977) consisting of a
system of delay differential equations. For the Petri dish, the focus is on the spread of virus infection of
immobilized bacteria in agar in the form of a moving front and thus we have a reaction-diffusion equation
with time-delay. In both cases, the delay represents the virus latent period in an infected cell. The size
of the resulting plaque after a fixed time, and therefore, the speed of the front, is one observable that is
used to identify either bacteria or virus and therefore is of interest. In marine environments where there
are many virus and microbe “species”, it has recently been noted that virus may have sizeable host ranges
and that the infection network, who infects who, often has a nested structure. Our work shows that such
communities are persistent and can be assembled by sequential addition of one new species at time. In
doing so, we ignore virus latency, simplifying to a large system of ordinary differential equations.
Optimizing Biogas Generation using Anaerobic Digestion
Gail S. K. Wolkowicz (Lord Robert May Award talk)
Department of Mathematics and Statistics
McMaster University
E-mail: [email protected]
This is joint work with Marion Weedermann of Dominican University and Gunog Seo of Colgate University.
Anaerobic digestion is a complex naturally occurring process during which organic matter is broken
down into biogas and various byproducts in an oxygen-free environment. It is used for waste and wastewater
treatment and for production of such biogases as methane than can be used to produce energy from animal
waste. A system of differential equations modelling the interaction of microbial populations in a chemostat
is used to describe three of the four main stages of anaerobic digestion: acidogenesis, acetogenesis, and
methanogenesis. To examine the effects of the various interactions and inhibitions, we first study an
inhibition-free model and obtain results for global stability using differential inequalities together with
conservation laws. These results are compared with the predictions for the model with inhibition. A case
study illustrates the effect of inhibition on the regions of stability. In particular, inhibition introduces
regions of bistability and stabilizes some equilibria. Implications for optimizing biogas production are then
explored. We show that the highest biogas production usually occurs for control parameters that result
in a bistable state. As well, surprisingly, the optimal biogas production does not always occur at a steady
state where all the different classes of microorganisms coexist. In some regions of bistability there is biogas
production at only one of the steady states, but in some regions although both steady-states result in
biogas production, one state is much more productive than the other. We show which control parameters
and changes in initial conditions the model predicts can move the system to or from the optimal state.
12
ICMA-V, October 2-4, 2015
Abstracts II-1——Plenary Talks
Treatment-Donation-Stockpile Dynamics in Convalescent Blood Transfusion Therapy
Jianhong Wu
Department of Mathematic and Statistics
York University
E-mail: [email protected]
This involves collaboration with Xi Huo, Kunquan Lan, Xiaodan Sun and Yanyi Xiao. The interim
guidance issued by the World Health Organization during the West Africa 2014 Ebola outbreak provides
guidelines on the use of convalescent blood from Ebola survivors for transfusion therapy. It is critically
important to have an appropriate mathematical model, based on the interim guidance, to examine the
transmission-treatment-donation-stockpile dynamics during an Ebola outbreak and with a large scale use of
the transfusion therapy in the population. Among many potential applications, we show this model should
be useful for us to estimate the reduction of case fatality ratio by introducing convalescent blood transfusion
as a therapy, and inform optimal treatment-donation-stockpile strategies to balance the treatment need
for case fatality ratio reduction and the strategic need of maintaining a minimal blood bank stockpile for
other control priorities.
13
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
The Role of CD4 T Cells in Immune System Activation and Viral Reproduction in a Model
for HIV Infection
Pooya Aavani
Department of Biological Science
Texas Tech University
E-mail:[email protected]
CD4 T cells play a fundamental role in the adaptive immune response including activation of naive B
cells and macrophages and recruitment of neutrophils and macrophages to the site of infection. Human
immunodeficiency virus (HIV) which infects and kills CD4 T cells, causes progressive failure of the immune
system. However, HIV particles are also reproduced by the infected CD4 T cells. Therefore, during HIV
infection, infected and healthy CD4 T cells act in opposition to each other, reproducing virus particles
and activating humoral and cellular immune responses, respectively. In this investigation, we develop
and analyze a simple system of four ordinary differential equations that accounts for these two opposing
roles of CD4 T cells. The model illustrates the importance of the adaptive immune response during
the asymptomatic stage of HIV infection. In addition, the solution behavior exhibits the three stages of
infection, acute, asymptotic and final AIDS stage.
Ecological benefits of CRISPR-CAS systems to bacterial colonies in the presence of phage
infection
Qasim Ali and Lindi M. Wahl
Department of Applied Mathematics
University of Western Ontario
E-mail: [email protected]
Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR), linked with CRISPR as- sociated (CAS) genes, play a profound role in evolving bacteria. It is now well understood that CRISPR-CAS
systems can confer adaptive immunity to bacteriophage infection. This is acheived by storing part of the
phage genome, the protospacer, in the bacterial genome such that the same virus can be recognized in
future and possibly controlled. However, the possibility of CRISPR system failure may lead to a productive infection by the phage (cell lysis) or lysogeny. Recently, CRISPR-CAS genes have been implicated in
changes to the mobility and group behaviours of the bacterium Pseudomonas aeruginosa, when lysogenized
by bacteriophage DMS3. In particular, the presence of the protospacer and protospacer adjacent motif
(PAM) of the DMS3 prophage were found to be necessary and sufficient to inhibit the biofilm formation
ability and swarming motility of P. aeruginosa. This result suggests that the CRISPR-CAS system imposes
a “quarantine” on lysogenized bacteria, which may be an effective strategy for the colony in the face of
phage pressure. Here, we study the ecological and evolutionary effects of this strategy by modelling phage
infection dynamics in a population of bacteria that have the ability to form a biofilm when not lysogenized. Quantitative parameter estimates have been obtained from the primary experimental literature
where possible. Preliminary results suggest that this self-quarantine of bacteria with prophage helps to
completely eradicate the phage infection regardless of bacteria inside or outside biofilm while bacteria with
CRISPR-CAS immunity survives.
14
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Estimation of the Probability of Invasion and the Time to Invasion Failure in Markov
Chain Models of Populations and Epidemics
Linda J. S. Allen and William Tritch
Department of Mathematics and Statistics
Texas Tech University
E-mail: [email protected]
If the number of individuals introduced into a native population is relatively small, the invasion may
be unsuccessful. Such is also the case for the introduction of a small number of infectious individuals into a
susceptible population. Theory from birth and death processes and branching processes can be applied to
estimate the probability of an invasion and the distribution for the time to failure in Markov chain models.
The birth and death rates at the time of invasion are critical parameters in defining the probability of
invasion and the time to failure. Examples are given to illustrate how the theory applies in competition
and in epidemic models.
An Extension of the Fisher-Wright Model
with Longer Coexistence Times
MattheW Badali and Anton Zilman
Department of Physics
University of Toronto
E-mail: [email protected]
The Moran-Wright-Fisher (MWF) model is a classical model of stochastic population evolution that
shows that in a population expressing two traits, one of them disappears from the population even in
the case of neutral evolution: an event called fixation. The simplifying assumptions of the MWF model
are that the divisions of all individuals are synchronous, resulting in discrete generation times, and that
the population size remains constant. We extend the MWF model to asynchronous reproduction and
continuous time, and remove the fixed population constraint. The model presented in this talk consists of
a pair of logistic growth processes coupled in their death terms by a variable parameterizing the overlap
of their ecological niches. If a trait allows for the use of different resources then the niche overlap is lower,
hence there is weaker competition. The total population is allowed to fluctuate, although it does so about
a mean system size, characterized by a carrying capacity. Using the backward master equation method to
provide arbitrarily precise solutions of the mean fixation time of this system, we investigate the transition
between two limits. In the limit of complete niche overlap, the fixation time of the coupled logistic system
matches that of the MWF model. In the other limit, the two traits coexist for exponentially long times as
a function of the system size.
15
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
A model for the propagation of malaria between two populations
Jacques Bélair1,2,3,4 and Fidèle Niyukuri1
Département de mathématiques et de statistique,
2 Centre de recherches mathématiques
Université de Montréal
Centre for applied mathematics in biosciences and medicine (CAMBAM), McGill University
4 Centre for disease modelling (CDM), York University
E-mail: [email protected]
1
3
A discrete-time mathematical model for the spread of malaria is developed to determine the influence
that a population shift from rural to urban areas may have on the persistence, or reduction, of the disease.
The model, a system of fourteen finite-difference equations, is analyzed and the reproductive number R0
is explicitly determined and shown to take the form of a maximum of two quantities related to specific
subpopulations. The model is then compared with a recent continuous time (ODE) model.
Age Before Bee-auty: An Age-Structured Model of Honey Bees, Disease, and
Environmental Hazards
M. Betti, L.M. Wahl, M. Zamir
Department of Applied Mathematics
University of Western Ontario
E-mail: [email protected]
The global decline of honey bee populations has been a persistent problem in recent history, with
potentially detrimental effects on agriculture. The current consensus is that this problem is multi-faceted
and pesticide use as well as disease may contribute to colony collapse [1]. We have recently proposed
a model which combines the dynamics of the spread of disease within a bee colony with the underlying
demographic dynamics of the colony, including both hive bees and foraging bees [2]. This model shows
the drastic effects of disease on a colony and how environmental hazards can exacerbate this problem. We
extend this model to incorporate the age sensitive dynamics of a honey bee colony. The individual ages
of the bees in a hive play a large part in the the effectiveness in their role within the hive. Our model
shows the age distribution for a healthy hive. We are able to solve this PDE system analytically, and show
global asymptotic stability to the equilibrium distribution in the face of exclusively environmental hazards.
Moreover, we derive an expression for the basic reproduction number of an infection within the hive. We
also simulate different types of diseases within a hive and show that these diseases can be diagnosed based
on the age profile of the hive.
[1 ] D. vanEngelsdorp, J. D. Evans, C. Saegerman, et al. Colony collapse disorder: A descriptive study.
PLoS ONE, (4)8: e6481, (2009).
[2 ] M. I. Betti, L. M. Wahl, M. Zamir. Effects of Infection on Honey Bee Population Dynamics: A
Model. PLoS ONE, 9(10): e110237, (2014).
16
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
La Crosse Virus Encephalitis: Understanding Disease Dynamics at the Interface Between
Epidemiology and Invasion Biology
Sharon Bewick1 , Folashade Agusto2 , Justin M. Calabrese3 , Ephantus J. Muturi4 and William F. Fagan1
1 Department of Biology, University of Maryland
2 Department of Mathematics, Austin Peay State University
3 Conservation Ecology Center, Smithsonian Conservation Biology Institute
4 Center for Ecological Entomology, Illinois Natural History Survey
E-mail:[email protected]
La Crosse encephalitis is a mosquito-borne viral disease that has recently emerged in new locations
across Appalachia. Conventional wisdom suggests that the recent uptick in La Crosse cases could be a result
of the invasive Asian Tiger Mosquito. Efforts to prove such an assumption, however, are complicated by the
large number of different transmission routes and species interactions involved in La Crosse virus dynamics.
For example, whereas most commonly studied mosquito-borne diseases are primarily transmitted from
host to vector and back, La Crosse encephalitis additionally exhibits efficient transovarial transmission.
This makes analysis of disease transmission cycles more difficult. Another complication is competition
between the native and invasive vectors. Because these two mosquitoes differ in their abilities to transmit
virus, disease spread can be impacted by the degree of displacement of the native vector by its invasive
competitor. We analyze the dynamics of La Crosse encephalitis by constructing epidemiological models
to describe the various processes maintaining La Crosse virus in wildlife reservoirs, both in the native
system and in systems that have been invaded by the tiger mosquito. Surprisingly, our analysis shows
that the tiger mosquito should, if anything, reduce transmission of La Crosse encephalitis. This is true for
both transmission within wildlife reservoirs and transmission to humans. We thus conclude that the tiger
mosquito may not be responsible for the increase in La Crosse encephalitis in Appalachia, and that other
factors, for example different invasive mosquitoes or changes in climatological variables and/or wildlife
densities, should be considered as alternative explanations.
Optimal mutation rates for parasite exploitation in an seasonal epidemic model
1
Ben Bolker1 and Michael D. Birch2
Departments of Mathematics & Statistics and Biology, McMaster University
2 Department of Physics, McMaster University
E-mail: [email protected]
We consider the evolution of mutation rate in a seasonally forced, deterministic, compartmental epidemiological model with a transmission-virulence trade-off. The evolutionarily stable (ESS) mutation rate
is the one which drives the lowest average density, over the course of one forcing period, of susceptible
individuals at steady state. In contrast with earlier eco-evolutionary models in which higher mutation
rates allow for better evolutionary tracking of a dynamic environment, numerical calculations suggest that
in our model the minimum average susceptible population, and hence the ESS, is achieved by a pathogen
strain with zero mutation.
17
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Overcompensatory dynamics in IDEs
Adèle Bourgeois
Department of Mathematics and Statistics
University of Ottawa
E-mail:[email protected]
We consider integrodifference equations (IDEs), which are of the form
Z
Nt+1 (x) = K(x − y)F (Nt (y)) dy,
where K is a probability distribution and F a growth function. It is already known that for monotone
growth functions, solutions of the IDE will have spreading speeds and are sometimes in the form of travelling
waves. We are interested in studying the case where F is a function with overcompensatory dynamics, i.e.
p-point cycles can appear for certain parameter values, eventually leading into chaos. Such is the case for
the Ricker function. This topic was first introduced in [1]. It was claimed that when F manifests a stable
p-point cycle, the solution of the IDE alternates between p profiles, all the while moving with a certain
spreading speed. However, simulations revealed that not only do the profiles alternate, but the solution is
a succession of p travelling objects with different spreading speeds. Using the theory from [?], we can prove
this and establish the theoretical formulas for the spreading speeds that exist within the different parts of
the solution. Those results can then be compared with numerical simulations. The existence of successive
travelling objects within a solution will also allow us to relate to the theory of dynamic stabilization in
continuous systems.
[1 ] M. Kot, Discrete-time traveling waves: Ecological examples, Journal of Mathematical Biology. 30,
pp. 413-436 (1992).
[2 ] H. F. Weinberger, Long-time behavior of a class of biological models, SIAM Journal on Mathematical
Analysis. 13, pp. 353-396 (1982).
Age of Infection Epidemic Models
Fred Brauer
Department of Mathematics
University of British Columbia
E-mail: [email protected]
The age of infection epidemic model, first introduced by Kermack and McKendrick in 1927, is a general
structure for compartmental epidemic models. It is possible to estimate the basic reproduction number if
the initial exponential growth rate and the infectivity as a function of time since being infected are known,
and this is also possible for models with heterogeneous mixing. This also extends to models for diseases
such as cholera with both direct and indirect transmission of infection.
18
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Competitive spatially distributed population dynamics models: does diversity in diffusion
strategies promote coexistence?
Elena Braverman
Department of Mathematics and Statistics
University of Calgary
E-mail: [email protected]
We study the interaction between different types of dispersal, intrinsic growth rates and carrying capacities of two competing species in a heterogeneous environment: one of them is subject to a regular diffusion
while the other moves in the direction of most per capita available resources. If spatially heterogeneous
carrying capacities coincide, and intrinsic growth rates are proportional then competitive exclusion of a
regularly diffusing population is inevitable. However, the situation may change if intrinsic growth rates for
the two populations have different spatial forms. We also consider the case when carrying capacities are
different. If the carrying capacity of a regularly diffusing population is higher than for the other species,
the two populations may coexist; as the difference between the two carrying capacities grows, competitive
exclusion of the species with a lower carrying capacity occurs. This is a joint work with Md. Kamrujjaman
and L. Korobenko.
Conservative Plankton Models with Time Delay
Sue Ann Campbell
Department of Applied Mathematics
University of Waterloo
E-mail:[email protected]
We consider a three compartment (nutrient-phytoplankton-zooplankton) model with nutrient recycling.
When there is no time delay the model has a conservation law and may be reduced to an equivalent two
dimensional model. We consider how the conservation law is affected by the presence of a time delay and
diffusion. We study the stability and bifurcations of equilibria when the total nutrient in the system and
the time delay are used as bifurcation parameters. This is joint work with Matt Kloosterman and Francis
Poulin.
Generation Interval Distributions
David Champredon and Jonathan Dushoff
School of Computational Science and Engineering
McMaster University
E-mail:[email protected]
In epidemiology, the generation interval is the interval between the time that an individual is infected
by an infector and the time this infector was infected. Its distribution often underpins estimates of the
reproductive number (the number of secondary cases from an index case) and hence public health strategies. Empirical generation interval distributions are often derived from contact tracing or clinical data.
But linking contact-tracing data to the generation interval for modelling purposes is unfortunately not
straightforward, and misspecifications can lead to incorrect estimates of the reproductive number. Our
work clarifies the theoretical framework for three conceptually different generation intervals distribution:
the intrinsic one typically used in mathematical models and the forward and backward ones typically observed from contact tracing data, looking respectively forward or backward in time. We apply our theory
to simulated data and highlight the pitfalls of using incorrectly empirical generation interval distributions
into mathematical models.
19
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
A delayed HIV-1 model with virus waning
Yuming Chen
Department of Mathematics
Wilfrid Laurier University
E-mail:[email protected]
In this talk, we propose and analyze a delayed HIV-1 model with CTL immune response and virus
waning. The two discrete delays stand for the time for infected cells to produce viruses after viral entry
and for the time for CD8+ T cell immune response to emerge to control viral replication. We obtain
the positiveness and boundedness of solutions and find the basic reproduction number R0 . If R0 < 1,
then the infection-free steady state is globally asymptotically stable and the infection is cleared from the
T-cell population; whereas if R0 > 1, then the system is uniformly persistent and the viral concentration
maintains at some constant level. The global dynamics when R0 > 1 is complicated. We establish the
local stability of the infected steady state and show that Hopf bifurcation can occur. Both analytical and
numerical results indicate that if, in the initial infection stage, the effect of delays on HIV-1 infection is
ignored, then the risk of HIV-1 infection (if persists) will be underestimated. Moreover, the viral load
differs from that without virus waning. These results highlight the important role of delays and virus
waning on HIV-1 infection. This is a joint work with Dr. Shengqiang Liu (Harbin Institute of Technology,
China) and his two PhD students, Bing Li and Xuejuan Lu.
Adaptive dispersal effect on the spread of a disease in a patchy environment
Chang-Yuan Cheng
Department of Applied Mathematics
National Pingtung University
E-mail :[email protected]
During outbreaks of a communicable disease, people intensely follow the media coverage of the epidemic.
Most people attempt to minimize contact with others, and move themselves to avoid crowds. This dispersal
may be adaptive regarding the intensity of media coverage and the population numbers in different patches.
We propose an epidemic model with such adaptive dispersal rates to examine how appropriate adaption can
facilitate disease control in connected groups or patches. Assuming dependence of the adaptive dispersal on
the total population in the relevant patches, we derived an expression for the basic reproduction number
R0 to be related to the intensity of media coverage, and we show that the disease-free equilibrium is
globally asymptotically stable if R0 < 1, and it becomes unstable if R0 > 1. In the unstable case, we
showed a uniform persistence of disease by using a perturbation theory and the monotone dynamics theory.
Specifically, when the disease mildly affects the dispersal of infectious individuals and rarely induces death,
a unique endemic equilibrium exists in the model, which is globally asymptotically stable in positive
states. Moreover, we performed numerical calculations to explain how the intensity of media coverage
causes competition among patches, and influences the final distribution of the population.
20
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
HIV Viral Rebound Following Therapy Suspension: Stochastic Model Predictions
Jessica M. Conway
Department of Mathematics
Pennsylvania State University
E-mail: [email protected]
Suspension of antiretroviral therapy (ART) for HIV typically leads to rapid viral load rebound to pretherapy levels. However, reports suggest that if ART is initiated early, viral rebound following therapy
suspension may be significantly delayed or, potentially, prevented (termed post-treatment control). We
present a model of HIV dynamics following cessation of therapy. From a branching process model formulation we derive the probability density functions describing viral rebound times. We use this to make
clinically-relevant predictions on expected times to viral rebound and on the probability of post-treatment
control.
Interpretation and modelling with super-resolution microscopy
Daniel Coombs
Department of Mathematics and Institute of Applied Mathematics
University of British Columbia
E-mail: [email protected]
New microscopic imaging techniques yield precise positional information of fluorescent markers down to
the scale of tens of nanometers and provide beautiful qualitative images of cellular structures. In this talk I
will discuss our ongoing work on one such technique, Stochastic Optical Reconstruction Microscopy. I will
describe the technique, highlighting a particular challenge to obtaining quantitative information from the
data, describe how we are addressing that challenge using a hidden Markov model, and also point out some
interesting problems that are not completely resolved. The work will be illustrated using experimental data
from cell-surface receptors on B cells and cardiac myocytes and I will outline how the microscopic data is
informing new models of signaling in both cases. This is joint work with Alejandra Herrera, Libin Abraham
and Ki-Woong Sung and members of the Edwin Moore, Keng Chou and Michael Gold labs at UBC.
21
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
The reduction principle, the ideal free distribution, and the evolution of dispersal strategies
Chris Cosner
Department of Mathematics
University of Miami
E-mail:[email protected]
The problem of understanding the evolution of dispersal has attracted much attention from mathematicians and biologists in recent years. For reaction-diffusion models and their nonlocal and discrete
analogues, in environments that vary in space but not in time, the strategy of not dispersing at all is
often convergence stable within in many classes of strategies. This is related to a ?reduction principle?
which states that that in general dispersal reduces population growth rates. However, when the class of
feasible strategies includes strategies that generate an ideal free population distribution at equilibrium (all
individuals have equal fitness, with no net movement), such strategies are known to be evolutionarily stable
in various cases. Much of the work in this area involves using ideas from dynamical systems theory and
partial differential equations to analyze pairwise invasibility problems, which are motivated by ideas from
adaptive dynamics and ultimately game theory. The talk will describe some past results and current work
on these topics.
Evolutionary game theory under time constraint
Ross Cressman
Department of Mathematics
Wilfrid Laurier University
E-mail:[email protected]
Evolutionary game theory was developed under a number of simplifying assumptions. One that is not
often explicitly stated is that each interaction among individuals takes the same amount of time no matter
what strategies these individuals use. When interaction time is strategy-dependent, it is more realistic to
take individual fitness as the payoff received per unit time. For instance, two Hawks interacting in the
standard two-player Hawk-Dove game are assumed to engage in a fight, implying that they will be involved
in fewer interactions than Doves since they avoid such contests.
Such effects have been taken into account in classical foraging theory models of optimal predator
behavior. I will briefly explain how optimization results for classical diet choice and patch choice models
(including those that involve the effects of simultaneously encountering different types of prey and of prey
recognition effects) can be reinterpreted as Nash equilibrium solutions of time-constrained evolutionary
games. I will also explore how interaction times affect the evolutionary outcome (e.g. the evolutionarily
stable strategy (ESS) and stability of the replicator equation) in the Hawk-Dove game. If time permits,
I will show that cooperation can evolve in the repeated Prisoner’s Dilemma game when the number of
rounds is under the players’ control.
22
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
On the dynamics of an evolutionary population dynamic model and life history adaptations
to climate change
J. M. Cushing
Department of Mathematics and Interdisciplinary Progrm in Applied Mathematics
University of Arizona
E-mail:[email protected]
I apply a bifurcation theorem for a class of evolutionary matrix equations with primitive projection
matrices to a model motivated by changes in certain life history strategies observed in marine bird colonies
in response to climate change. The fundamental question is under what circumstances the model will
predict successful adaptation to climate change and with what resulting dynamic.
A PDE model for the evolution of epigenetically inherited drug resistance
Troy Day
Department of Mathematics and Statistics, Department of Biology
Queen’s University
E-mail: [email protected]
Epigenetic inheritance is the transmission of nongenetic material such as gene expression levels, mRNA,
and other biomolecules from parents to offspring. There is a growing realization that such forms of
inheritance can play an important role in evolution. Bacteria represent a prime example of epigenetic
inheritance because a large array of cellular components are transmitted to offspring, in addition to genetic
material. For example, there is an extensive and growing empirical literature showing that many bacteria
can become resistant to antibiotics within acquiring any genetic changes. In this talk I will show how a PDE
model of such epigenetically inherited drug resistance can account for many of the empirical observations
in the literature.
23
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
A Model of Microtubule Organization in the Presence of Motor Proteins
Gerda de Vries
Department of Mathematical & Statistical Sciences
University of Alberta
E-mail: [email protected]
Microtubules and motor proteins interact in vivo and in vitro to form higher-order structures such as
bundles, asters, and vortices. In vivo, the organization of microtubules is connected directly to cellular
processes such as cell division, motility, and polarization. To address questions surrounding the mechanism
underlying microtubule organization, we have developed a system of integro-partial differential equations
that describes the interactions between microtubules and motor proteins. Our model takes into account
motor protein speed, processivity, density, and directionality, as well as microtubule treadmilling and reorganization due to interactions with motors. Our model is able to provide a quantitative and qualitative
description of microtubule patterning. Simulations results show that plus-end directed motor proteins
form vortex patterns at low motor density, while minus-end directed motor proteins form aster patterns at
similar densities. Also, a mixture of motor proteins with opposite directionality can organize microtubules
into anti-parallel bundles such as are observed in spindle formation.
Dynamics of an SIS epidemic reaction-diffusion model
Keng Deng
Department of Mathematics
University of Louisiana
E-mail: [email protected]
In this talk, we study an SIS reaction-diffusion model with spatially heterogeneous disease transmission
and recovery rates. A basic reproduction number R0 is defined for the model. We first prove that there
exists a unique endemic equilibrium if R0 > 1. We then consider the global attractivity of the disease-free
equilibrium and the endemic equilibrium for two cases. If the disease transmission and recovery rates are
constants or the diffusion rate of the susceptible individuals is equal to the diffusion rate of the infected
individuals, we show that the disease-free equilibrium is globally attractive if R0 ≤ 1, while the endemic
equilibrium is globally attractive if R0 > 1.
24
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Global dynamics of multi-group epidemic models with non-strongly connected transmission
networks
Peng Du
Department of Mathematical and Statistical Sciences
University of Alberta
[email protected]
We investigate the dynamics of multi-group epidemic models with transmission networks that are not
assumed to be strongly connected. We show mixed equilibria, at which some groups are disease-free
while others are endemic, can exist if the transmission network is not strongly connected. Considering a
condensed digraph by collapsing each strongly connected component, we are able to define an evaluation
function on the set P of all equilibria, and show that all solutions converge to an unique equilibrium P ∗
which is the maximizer of the evaluation function. The approach is general, it can be applied to various
mathematical models from epidemiology and spatial ecology.
Determining viral load set point and time to reach viral load set point among patients
infected with HIV-1 subtypes A, C and D
D.W. Dick, L.M. Wahl
Department of Applied Mathematics
University of Western Ontario
E-mail: [email protected]
Viral load set point and time to reach viral load set point after acute infection are valuable metrics
with which to characterize HIV disease progression. Understanding differences in disease progression
among HIV subtypes is important as most HIV research focuses on HIV-1 subtype B, which is prevalent in
North America and Western Europe. However HIV-1 subtype C is predominant in Africa and the global
prevalence of subtype C has grown to make up 51% of all HIV-1 infections worldwide [1].
Using data from a 10-year longitudinal study in Zimbabwe and Uganda, we introduce a definition of
time to viral load set point to estimate and compare set point and time to set point in 301 women infected
by HIV-1 subtypes A, C and D.
An in-host model of disease progression is considered to explore mechanisms that may generate the
observed differences in set point and time to set point among HIV-1 subtypes. Differences in disease
progression among subtypes and in the mechanisms that are responsible for these differences may have
important implications for disease transmission, the rapid spread of HIV-1 subtype C and the global HIV
epidemic more generally.
[1 ] Denis M Tebit and Eric Arts, Tracking a century of global expansion and evolution of HIV to drive
understanding and combat disease, Lancet Infect Dis. 11, pp. 45-56 (2011).
25
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Initial growth rate, generation intervals and reproductive numbers in the spread of
infectious disease
Jonathan Dushoff
Department of Biology
McMaster University
E-mail:[email protected]
Two fundamental quantities that underlie understanding of disease spread are the basic reproductive
number, which gives the number of new cases caused by a ”typical” case in a predominantly susceptible
population, and the exponential growth rate, which gives asymptotic rate of disease growth, also in a
predominantly susceptible population. These quantities are linked by ”generation intervals”, which describe
the length of time between when an individual becomes infected, and when he or she infects others. I will
discuss the linked estimation of these three quantities, and some approximations and interpretations, with
applications to the recent West African Ebola epidemic, and to control of HIV.
Patterns of plague in London over four centuries
David Earn
Department of Mathematics & Statistics
McMaster University
E-mail:[email protected]
The city of London, England, sufferred outbreaks of plague from the 14th to 17th centuries. I will
discuss and compare the dynamical characteristics of these plagues, from the Black Death in 1348 to the
Great Plague of London in 1665, emphasizing the inferences that can be made from transmission modelling.
26
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Cross-diffusion in multispecies biofilms
Hermann J. Eberl1 , Kazi A. Rahman1 , Stefanie Sonner2 , Ranga Sudarsan1
1 Department of Mathematcs and Statistics, University of Guelph
2 Felix-Klein-Center, University of Kaiserlautern
E-mail:[email protected]
Bacterial biofims are microbial depositions on immersed interfaces. In many instances in nature these
form multi-species populations. Taking the view point of biofilms as spatially structured microbial populations, we have previoulsy given a derivation of a multi-species biofilm model that starts from a discrete
lattice master-equation for interacting species and lead to a cross-diffusion equation. In this talk we give
an alternative derivation of the same model, which, however, takes the view point of biofilm communities
as mechanical objects, starting form continuous mass and momentum balances. This presents itself as a
closure problem, which we solve by an algebraic biomass-pressure relationship.
Biologically and physically important, but mathematically not obvious, is that biomass densities remain negative and that an a priori known maximum biomass density cannot be exceeded. We will briefly
comment on this aspect and sketch a proof that shows that the proposed model indeed satisfies these
requirements.
We present numerical simulations that show that the proposed-cross-diffusion model overcomes a limitation of an earlier diffusion-reaction biofilm model without cross-diffusion and of earlier celluar automata
models, in that mixing of species is considerably de-emphasized and that the model is able to predict gradients in the species distribution within a biofilm colony. We also show that the proposed model overcomes
a limitation of an earlier model that starts from the same continuous mass and momentum balance but
was closed differently (leading to a hyperbolic-elliptic free boundary value problem) and did not allow for
mixing of species in a colony.
Hierarchical competition models with the Allee effect and immigration
Saber Elaydi
Department of Mathematics
Trinity University
E-mail: [email protected]
In this talk, we give a complete determination of the global dynamics of a hierarchical multi-species
model with the Allee effect and immigration. By a hierarchical model, we mean a dynamical system model
with a networked hierarchy of state variables rather than the random parameter models of statistics.
These types of models may be generated by maps of the form F : R+ N → R+ N , where F (x1 , x2 , ..., xN ) =
(f1 (x1 ), f2 (x1 , x2 ), ..., fN (x1 , x2 , ..., xN )). Hence these models may be given by the difference equation
Xt+1 = F (Xt ). In the dynamical system literature, these maps are called triangular maps, since their
Jacobian matrix is lower triangular. Then we show how immigration to one or more species would change
drastically the dynamics of the system. In particular, we show that if the level of immigration to one or
more species is above a specified level, then there would be no extinction region in which all species go to
extinction.
27
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Connecting Local Movement of Mule Deer with Regional Spread of Chronic Wasting
Disease
Martha Garlick
Department of Mathematics and Computer Science
South Dakota School of Mines and Technology
E-mail: [email protected]
Chronic Wasting disease (CWD) is an infectious, slow-developing prion disease that affects mule deer,
as well as white-tailed deer, elk, and moose. This fatal disease is of particular concern to wildlife managers
because of the potential impact to mule deer populations, as well as ecosystems. Spatial models can be
very useful in studying the spread of CWD, but as environments become increasingly fragmented, it is
important to make a connection between deer movement and landscape structure. Ecological diffusion
models accomplish this connection, but need variable motility coefficients (with units of area per time).
We develop a method to estimate these coefficients from landscape classification and GPS location data.
Human behaviour and infectious disease transmission: a hybrid system approach
S.W. Greenhalgh1,2 , M.-G. Cojocaru3 , C.T. Bauch4 , D. Yamin1 , A.P. Galvani1
1
2
Department of Mathematics & Statistics
Queen’s University
Center for Infectious Disease Modeling and Analysis
Yale University
3 Department of Applied Mathematics
University of Waterloo
4 Department of Mathematics & Statistics
University of Guelph
E-mail:[email protected]
Understanding the interplay between human behaviour and the spread of infectious disease is instrumental to the successful implementation of health policy, yet challenging to reach. For example, human
behaviour impacts disease transmission, which in turn can further affect behaviour. Thus, a theoretical
extension of compartmental models is needed to account for the complex coupling of human behaviour
with infectious disease transmission. Here we present a hybrid systems framework to model the interaction
of human behaviour and infectious disease transmission. First, we present the hybrid system framework
for a typical susceptible-infected-recovered model. Then, we show applications of hybrid systems: the integration of vaccination decisions in response to H1N1 incidence; and the implementation of the Center for
Disease Control and Preventions Emergency Preparedness and Response plan in response to a hypothetical
smallpox bioterror attack.
28
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Vaccination, Screening, Treatment and Bifurcations
Jane Heffernan
Department of Mathematics and Statistics
York University
E-mail:[email protected]
Vaccination, screening and treatment programs have one common aim to control the severity of infection in individuals and the population. Mathematical modelling studies of infectious disease and public
health control strategies are used to determine characteristics of vaccination, screening and treatment programs that must be met to prevent or minimize the impact of infection. Typically, the control threshold
lies solely on the Basic Reproductive Ratio, however, backward bifurcations and regions of chaos may complicate matters. We will discuss vaccination, treatment and screening models of some childhood diseases,
and sexually transmitted infections. Implications of different bifurcations on public health programs will
be discussed.
Effects of Warming Seas: Cannibalism and Reproductive Synchrony in a Seabird Colony
Shandelle M. Henson
Department of Mathematics
Andrews University
E-mail: [email protected]
Increased sea surface temperatures are associated with egg cannibalism and egg-laying synchrony in
glaucous-winged gulls. We pose a general discrete-time model for ovulation dynamics during the breeding
season and then extend it across multiple seasons. The model shows that in the presence of cannibalism
egg-laying synchrony can allow the population to persist at lower birth rates than would be possible without
synchrony.
Navigating the Flow: the Homing of Sea Turtles
Thomas Hillen
Department of Mathematical and Statistical Sciences
University of Alberta
E-mail: [email protected]
Navigation is challenging for most animals, yet water and airborne species face an additional hurdle
due to the surrounding flow, from persistent currents to highly unpredictable storms. In this talk we
formulate an individual-based model for navigation within a flowing field and apply scaling to derive its
corresponding macroscopic and continuous model. We apply it to various movement classes, from drifters
that simply go with the flow to navigators that respond to environmental orienteering cues. We apply the
homing of the marine green turtle Chelonia mydas to Ascension Island. (joint work with K.J. Painter,
Heriot Watt)
29
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Displacement of bacterial plasmids by engineered unilateral incompatibility
Brian Ingalls
Department of Applied Mathematics
University of Waterloo
E-mail: [email protected]
Bacterial plasmids employ copy number control systems to ensure they do not overburden their hosts.
Plasmid incompatibility is caused by shared components of copy number control systems, resulting in
mutual inhibition of replication. Incompatible plasmids cannot be stably maintained within a host cell.
Unilateral incompatibility, in which the plasmid replicons are compatible but one plasmid encodes for the
replication inhibitor of the other, leads to rapid displacement of the inhibited plasmid. Thus we propose
that unilateral incompatibility can be used to eradicate an undesirable plasmid from a population. To
investigate this process, we developed deterministic and stochastic models of plasmid dynamics. Analysis
of these models provides predictions about the efficacy of plasmid displacement.
A hybrid model for epidemics on a contact network using a pair approximation result
Karly Jacobsen
Mathematical Biosciences Institute
Ohio State University
E-mail: [email protected]
Heterogeneity in contact network structure is known to play an important role in the spread of epidemics. Models taking full network structure into account quickly become intractable as the size of the
network increases. Pair approximation techniques have been widely used but do not necessarily agree with
stochastic simulations for large graphs with increasing network complexity. An alternative edge-based compartmental model has been developed and rigorously proven to be the large volume limit of the exact SIR
stochastic system on a graph with a specified degree distribution. We explore the underlying cause of discrepancy between the exact edge-based system and the SIR model using a well-known pair approximation.
We determine a sufficient condition on the degree distribution, satisfied by several common distributions,
under which the exact system and the pair approximation model agree. Based on this result, we develop a
hybrid stochastic-deterministic model which allows for parameter estimation. Extensions of this framework
to a multitype model for Ebola will also be discussed.
30
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Prophylactic vaccination strategies for disease outbreaks on community networks
Michael R. Kelly
Department of Mathematics
The Ohio State University
E-mail: [email protected]
The risk of disease outbreaks within a network is important when considering where intervention
strategies should be focused. The problem is intensified when considering uncertainty among regions
within a network. We investigate questions of disease intervention, given uncertainty about the regions
and where an outbreak occurs. We first investigate scenarios where intervention is fast, not dependent
on time. We seek answers to the the problem of minimizing the costs while also lowering the expected
network reproduction number below some desired threshold. We compare results to outbreak scenarios
with intervention. This problem is relevant due to the current debate on vaccination campaigns and vaccine
stockpiles, with questions on how many doses to be requested and where vaccines should be deployed.
Modeling aspects of cancer stem cells
Mohammad Kohandel
Department of Applied Mathematics
University of Waterloo
E-mail:[email protected]
The cancer stem cell (CSC) hypothesis proposes that only a (typically small) sub-population of cells
has the capacity to proliferate indefinitely and hence to initiate and maintain tumour growth. According to
this model CSCs, in addition to their self-renewal, can undergo symmetric or asymmetric ”unidirectional”
divisions to generate daughter cells with low tumorigenic potential (non-CSCs). However, growing evidence
supports violation of unidirectionality for the traditional stem cell based tissue hierarchy, suggesting a new
model in which a significant degree of plasticity exists between the non-CSC and CSC compartments.
This talk will survey our mathematical approaches to investigate the CSC hypothesis and the dynamic
phenotypic switching between these populations, as well as therapeutic implications.
Persistence in Phage-Bacteria Communities with Nested and One-to-One Infection
Networks
Daniel A. Korytowski and Hal L. Smith
School of Mathematical and Statistical Sciences
Arizona State University
E-mail:[email protected]
We show that a bacteria and bacteriophage system with either a perfectly nested or a one-to-one infection network is permanent, a.k.a uniformly persistent, provided that bacteria that are superior competitors
for nutrient devote the least to defence against infection and the virus that are the most efficient at infecting host have the smallest host range. By ensuring that the density-dependent reduction in bacterial
growth rates are independent of bacterial strain, we are able to arrive at the permanence conclusion sought
by Jover et al (J. Theor. Biol. 332:65-77, 2013). The same permanence results hold for the one-to-one
infection network considered by Thingstad (Limnol Oceanogr 45:1320-1328, 2000) but without virus efficiency ordering. Additionally we show the global stability for the nested infection network, and the global
dynamics for the one-to-one network.
31
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Periodic Solutions of a Differential Equation with a Queueing Delay
Tibor Krisztin
Bolyai Institute
University of Szeged
E-mail :[email protected]
We consider a differential equation with a state-dependent delay motivated by a queueing process. The
time delay is determined by an algebraic equation involving the length of the queue. For the length of the
queue a discontinuous differential equation holds. We formulate an appropriate framework to study the
problem, and show that the solutions define a Lipschitz continuous semiflow in the phase space. Within
this framework we prove the existence of slowly oscillating periodic solutions.
This is a joint work with my PhD student, István Balázs.
A mutation-selection model for evolution of random dispersal
King-Yeung(Adrian) Lam
Department of Mathematics
Ohio State University
E-mail :[email protected]
We consider a mutation-selection model of a population structured by the spatial variables and a trait
variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal
in the trait variable. We focus on the asymptotic profile of positive steady state solutions. Our result
shows that in the limit of small mutation rate, the solution remains regular in the spatial variables and
yet concentrates in the trait variable and forms a Dirac mass supported at the lowest diffusion rate. [A.
Hastings, Theor. Pop. Biol., 24, 244-251, 1983] and [Dockery et al., J. Math. Biol., 37, 61-83, 1998] showed
that for two competing species in spatially heterogeneous but temporally constant environment, the slower
diffuser always prevails, if all other things are held equal. Our result suggests that their findings may hold
for arbitrarily many traits. This is joint work with Y. Lou (Ohio State and Renmin Univ.).
Persistence and Spreading Speeds of Integro-difference Equations with A Shifting Habitat
Bingtuan Li
Department of Mathematics
University of Louisville
E-mail:[email protected]
We discuss an integro-difference equation model that describes the spatial dynamics of a species in
a shifting habitat along which the species growth increases. We give conditions under which the species
disperses to a region of poor quality where the species eventually becomes extinct. We show that when the
species persists in the habitat, the rightward spreading speed and leftward spreading speeds are determined
by C, the speed at which the habitat shifts, as well as the dispersal kernel and species growth rates in both
directions. We demonstrate how C affects the spreading speeds. We also show that it is possible for a
solution to form a two-layer wave, with the propagation speeds of the two layers analytically determined.
32
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Staged-structured models for interactive mosquitoes
Jia Li
Department of Mathematical Sciences
The University of Alabama in Huntsville
E-mail:[email protected]
We present mathematical models for interactive wild and sterile mosquitoes, based on differential
equations. We include mosquitoes metamorphic stages, but simplify the models by grouping the three
aquatic stages into one class such that there are only two equations for the wild mosquitoes. Three
different strategies of releases of sterile mosquitoes are considered. We analyze the model dynamics and
provide numerical examples to demonstrate the dynamics.
Turning Points and Relaxation Oscillation Cycles in Simple Epidemic Models
Michael Li
Department of Mathematical and Statistical Sciences
University of Alberta
E-mail:[email protected]
We revisit the classical problem of periodicity in incidences of certain autonomous diseases. In a simple
SIR model with demography and disease-caused death, under the assumption that the host population
has a small intrinsic growth rate, and using singular perturbation techniques and the phenomenon of the
delay of stability loss due to turning points, we prove that large-amplitude relaxation oscillation cycles
exist for an open set of model parameters. Simulations are provided to support our theoretical results.
Our results offer new insight to the classical periodicity problem in epidemiology. Our approach relies on
analysis far away from the endemic equilibrium and contrasts sharply with the traditional method of Hopf
bifurcations. This is joint work with Weishi Liu of the University of Kansas, Chunhua Shan and Yingfei
Yi of the University of Alberta.
Finding the essential role of time delays
Wei Lin
School of Mathematical Sciences and CCSB
Fudan University
E-mail: [email protected]
Time delays are omnipresently existing in various real systems including biological, physical, and chemical systems. Two kinds of fundamental questions arises naturally. The first is how to find time delays
based only on the time series that are observed experimentally in real systems? And the second is what
kind of essential changes will time delays bring about? In this talk, with real datasets and biological models,
I will try to address these two questions.
33
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Stage-structured models of intra- and inter-specific competition within age classes
Yijun Lou
Department of Applied Mathematics
The Hong Kong Polytechnic University
E-mail:[email protected]
In some species, larvae and adults experience competition in completely different ways. Simple stagestructured models without larval competition usually yield a single delay equation for the adults. Using
an age structured system incorporating competition among both larvae and adults, we derive a system of
distributed delay equations for the numbers of larvae and adults. The system is neither cooperative nor
reducible to a single equation for either variable. Positivity, boundedness and uniform strong persistence
are established. Linear stability analysis of equilibria is difficult due to the strong coupling, but results
are proved for small delays using monotone systems theory and exponential ordering. For small delay we
prove a theorem on generic convergence to equilibria, which does not directly follow from standard theory
but can be proved indirectly using comparison arguments. Finally, we consider an extension to two-strain
competition and prove theorems on the linear stability of the boundary equilibria. This is joint work with
Profs. Jian Fang and Stephen Gourley.
Dispersal, stability, and synchrony in predator-prey metacommunities
Frithjof Lutscher
Department of Mathematics and Statistics, Department of Biology
University of Ottawa
E-mail: [email protected]
Predator-prey interactions can lead to oscillating population dynamics through a delayed, densitydependent negative feedback loop. These conditions are well understood in simple models, such as the
MacArthur-Rosenzweig model. When communities are spatially distributed, dispersal between sites creates
additional mechanisms that interact with the local feedback loop to affect the propensity for oscillations.
In addition, questions arise whether and how oscillations are synchronized in space.
In this talk, I will study a spatially coupled MacArthur-Rosenzweig model. I begin by showing that
two dispersal-related mechanisms (travel-time delay and density-dependent dispersal) in isolation act to
stabilize the community, but in conjunction can destabilize a steady state and lead to oscillations via a
Hopf bifurcation. Then I will show how these two mechanisms affect synchrony of oscillations between
patches. Specifically, I show that the ability of dispersal to synchronize populations is greatly diminished
by these two simple mechanisms, and I will propose a Hopf-bifurcation approach to asynchrony.
34
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
On the principle for host evolution in host-pathogen interactions
M. Martcheva, N. Tuncer, Y. Kim
Department of Mathematics
University of Florida
E-mail: [email protected]
We use a two-host one pathogen immuno-epidemiological model to argue that the principle for host
evolution, when the host is subjected to a fatal disease, is minimization of the case fatality proportion
F. This principle is valid whether the disease is chronic or leads to recovery. In the case of continuum
of hosts, stratified by their immune response stimulation rate a, we suggest that F(a) has a minimum
because a trade-off exists between virulence to the host induced by the pathogen and virulence induced
by the immune response. We find that the minimization of the case fatality proportion is an evolutionary
stable strategy (ESS) for the host.
An SEI Model with Immigration and Continuous Infection Age
Connell McCluskey
Department of Mathematics
Wilfrid Laurier University
E-mail: [email protected]
We consider an SEI model of disease transmission with age-in-class structure for the exposed and
infectious classes. The starting point for this is the model in [?]. To that, we add immigration of individuals
into all three classes. In particular, we allow that individuals may enter the exposed or infectious classes,
with a positive age-in-class. We get the following equations:
dS(t)
dt
= WS − µS S(t) −
R∞
0
β(a)S(t)i(t, a)da
∂e ∂e
+
∂t ∂a
= We (a) − (ν(a) + µe (a)) e(t, a)
∂i
∂i
+
∂t ∂a
= Wi (a) − µi (a)i(t, a),
with boundary conditions
e(t, 0) =
R∞
i(t, 0) =
R∞
0
0
(1)
β(a)S(t)i(t, a)da
(2)
ν(a)e(t, a)da
for t > 0. The age-in-class specific immigration rates are given by We (a) and Wi (a); other terms are
standard.
35
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Pathogen evolution under host avoidance plasticity
David McLeod
Department of Mathematics and Statistics
Queen’s University
E-mail:[email protected]
Host resistance consists of defenses that limit pathogen burden, and can be classified as either adaptations targeting recovery from infection or those focused upon infection avoid- ance. Conventional theory
treats avoidance as a fixed strategy which does not vary from one interaction to the next. However, there
is increasing empirical evidence that many avoid- ance strategies are triggered by external stimuli, and
thus should be treated as phenotypically plastic responses. Here we consider the implications of avoidance
plasticity for host-pathogen co-evolution. We uncover a number of predictions challenging current theory. First, in the absence of pathogen trade-offs, plasticity can restrain pathogen evolution; moreover, the
pathogen exploits conditions in which the host would otherwise invest less in resistance, causing resistance
escalation. Second, when transmission trades off with pathogen-induced mortality, plasticity encourages
avirulence, resulting in a superior fitness outcome for both host and pathogen. Third, plasticity ensures
the sterilizing effect of pathogens has conse- quences for pathogen evolution. When pathogens castrate
hosts, selection forces them to minimize mortality virulence; moreover, when transmission trades off with
sterility alone, resistance plasticity is suffcient to prevent pathogens from evolving to fully castrate.
Evolutionary stability in continuous nonlinear public goods games
Chai Molina (supervised by David J. D. Earn)
Department of Mathematics and Statistics
McMaster University
E-mail:[email protected]
We investigate a type of public goods game among groups of individuals who choose how much to
contribute towards the production of a common good, at a cost to themselves. In these games, the common
good is produced based on the sum of contributions from all group members, then equally distributed among
them. In applications, the dependence of the common good on the total contribution is often nonlinear
(e.g., exhibiting synergy or diminishing returns). To date, most theoretical and experimental studies have
addressed scenarios in which the set of possible contributions is binary or discrete. However, in many realworld situations, contributions are continuous (e.g., when individuals volunteer their time). The “n-person
snowdrift games” that we analyze involve continuously varying contributions. We establish under what
conditions populations of contributing (or “cooperating”) individuals can evolve and persist. Previous
work on snowdrift games, using adaptive dynamics, has found that an “equally cooperative” strategy—
contributing an equal share of the total necessary to maximize the benefit from the public good—is locally
convergently and evolutionarily stable. Using static evolutionary game theory, we find conditions under
which this strategy is actually globally evolutionarily stable. All these results refer to stability to invasion
by a single mutant. We broaden the scope of existing stability results by showing further that the equally
cooperative strategy is locally stable to potentially large population perturbations, i.e., allowing for the
possibility that mutants make up a non-negligible proportion of the population (e.g., due to genetic drift).
Lastly, as models of continuous snowdrift games typically rely on the assumption of an infinite population,
we investigate how these results are affected when the population size is finite.
36
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
A remark on the global dynamics of competitive systems on ordered Banach spaces
Daniel Munther
Department of Mathematics
Cleveland State University
E-mail: [email protected]
A well-known result in [Hsu-Smith-Waltman, Trans. AMS (1996)] states that in a competitive semiflow
defined on X + = X1+ × X2+ , the product of two cones in respective Banach spaces, if (u∗ , 0) and (0, v ∗ ) are
the global attractors in X1+ × {0} and {0} × X2+ respectively, then one of the following three outcomes is
possible for the two competitors: either there is at least one coexistence steady state, or one of (u∗ , 0), (0, v ∗ )
attracts all trajectories initiating in the order interval I = [0, u∗ ] × [0, v ∗ ]. However, it was demonstrated
by an example that in some cases neither (u∗ , 0) nor (0, v ∗ ) is globally asymptotically stable if we broaden
our scope to all of X + . In this talk, I’ll give two sufficient conditions that guarantee, in the absence of
coexistence steady states, the global asymptotic stability of one of (u∗ , 0) or (0, v ∗ ) among all trajectories
in X + . Namely, one of (u∗ , 0) or (0, v ∗ ) is (i) linearly unstable, or (ii) is linearly neutrally stable but zero
is a simple eigenvalue. These results complement the counter example mentioned in the above paper as
well as applications that frequently arise in practice. This is joint work with Adrian Lam (Ohio State
University).
Time Capsule Evolution: Recombination with Proviral DNA Promotes Viral Persistence
A. Nadeem and L.M. Wahl
Department of Applied Mathematics
Western University
E-mail: [email protected]
In recent years, experimental studies have demonstrated that the bacteria E. coli has the ability to
reduce the expression of receptors that harmful bacteriophages like Lambda phage can use as a point of
entry. It has also been observed that through natural selection, phages can acquire the ability to attach
to the host through a novel receptor instead of the ancestral one [2]. In rare cases, infecting phages can
recombine with provirus buried in the host’s genome by their temperate predecessors and utilize the new
information to overcome the host’s receptor-based defences (J. Meyer, personal communication). This
phenomenon raises a number of significant questions, such as whether the phage is adopting a long-term
strategy of burying provirus, rather than multiplying immediately through lysis? Does recombination with
provirus play a valuable role in ensuring the long-term persistence of the phage? To answer these questions
we have developed a differential equation model consisting of host cells with varying proportions of different
surface receptors, and viruses that may lysogenize their hosts (with a certain probability), inserting viral
genome sequences into the host cell DNA, which can be accessed by later generations of phage. The main
aim of the study is to evaluate how advantageous it is for the phage to use the host as a time capsule to
carry information that is detrimental to the host itself. These questions are of great significance as about
8% of the human genome is made up of proviral DNA [1].
[1 ] Casjens, Sherwood. ”Prophages and Bacterial Genomics: What Have We Learned so Far?” Molecular Microbiology 49.2 (2003): 277-300.
[2 ] Meyer, J. R., D. T. Dobias, J. S. Weitz, J. E. Barrick, R. T. Quick, and R. E. Lenski. ”Repeatability
and Contingency in the Evolution of a Key Innovation in Phage Lambda.” Science 335.6067 (2012):
428-32.
37
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Population dynamics in a producer-scrounger patch model
Andrew Nevai
Department of Mathematics
University of Central Florida
E-mail: [email protected]
The population dynamics of an ecological system involving producers and scroungers is studied using
a patch model. Producers can obtain the resource directly from the environment, but must surrender a
proportion of their discoveries to nearby scroungers through a process known as scramble kleptoparasitism.
Parameter combinations which allow producers and scroungers to persist either alone or together are distinguished from those in which they cannot. Producer persistence depends in general on the distribution
of resources and producer movement, whereas scrounger persistence depends on its ability to invade when
producers are at steady-state. It is found that both species can persist when the habitat has high productivity, only the producers can persist when the habitat has intermediate productivity, and neither species
can persist when the habitat has low productivity. This is joint work with C. Cosner and Z. Shuai.
Modelling intermediate filaments
Stèphanie Portet
Department of Mathematics
University of Manitoba
E-mail:[email protected]
Intermediate filaments are one of the components of cytoskeletal networks; they organize via a series
of assembly/disassembly and transport events. Understanding the assembly dynamics of intermediate
filaments, their organization in networks and resulting mechanical properties is essential to elucidate their
functions in cells. A combination of mathematical modelling and experimental data is used to investigate
the organization of the intermediate filament network in cells. What contributes to their organization?
What process or combination of processes does the organization emerge from? What process dominates?
38
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Mathematical modeling of honeybee populations, some of their diseases and other stressors
Hermann J. Eberl, Alex Petric, Vardayani Ratti, Richard Yam
Department of Mathematcs and Statistics
University of Guelph
E-mail: [email protected]
The Western honeybee is in trouble: Throughout North America and Europe, recent years have seen
tremendous colony losses, which depending how they manifest themselves have been characterized as
Colony Collapse Disorder (CCD, e.g. in the USA) or Wintering Losses (e.g. in Canada and many European countries). Several culprits have been suggested for this phenomenon, including disease, beekeeping
practices, and environmental stressors.
In this talk we give an overview of our modelling work on the topic. This accounts for stressors
such the ectoparasitic mite Varroa desructor and deadly viruses that it carries (we focus on the Acute
Bee Paralysis Virus), microsporidian diseases such as Nosema ceranae and Nosema apis, and exposure of
honeybees to environmental pesticides, in particular neonicotinoids. It also accounts for certain remedial
beekeeping strategies, such as varroacide applications and hive cleaning. An important aspect in honeybee
biology, that features prominently in our modelling work, is that population dynamics varies greatly with
the the seasons, leading to non-autonomous differential equations that are studied with analytical and
computational techniques.
This research program is joint work with Peter Kevan and Ernesto Guzman (School of Enviornmental Sciences, Univ Guelph), supported by the Ontario Ministry for Agriculture, Food and Rural Affairs
(OMAFRA).
Traveling Waves Solutions of Non-KPP Reaction-Diffusion Systems
Yuanwei Qi
Department of Mathematics
University of Central Florida
E-mail: [email protected]
In this talk, I shall present some recent results on the existence, multiplicity and bounds on traveling
wave solutions to a class of Reaction-Diffusion systems which have non-KPP nonlinearity and a linear
decay. We show how this combination of reaction-term has a deep influence of the structure of traveling
waves. These systems have wide range of applications in population dynamics, chemical waves and cellular
patterns in micro-biology.
This is a joint work with Xinfu Chen, X. Lai, C.Qin and Yajing Zhang.
39
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
A Location-Based Model for a Newly Proposed Class of Mobile Genetic Elements in
Prokaryotes: Mobile Promoters
M. Rabbani, Lindi M. Wahl
Department of Applied Mathematics
Western University
E-mail: [email protected]
Mobile promoters are a newly discovered sub-class of mobile genetic elements (MGEs). MGEs in general are DNA sequences which are able to insert themselves, or be inserted, at new sites in the genome(s).
MGEs themselves were long considered to be ”junk DNA” with no function and are typically regarded as
parasitical elements. In more recent years however, the importance of mobile genetic elements in genomic
evolution has received significant attention. In particular, evidence suggests that mobile elements play
an important role in alternations of genome architecture. Because of this impact in genome plasticity,
various mathematical and statistical models have been developed to describe the dynamics of these mobile
elements and to explore the biological factors effecting their dynamics during genome evolution.
In this work, we propose a new location-based model for the population dynamics of mobile promoters,
rooted in a newly proposed model by [1]. Here we extent the birth-death-diversification model, the first
model to incorporate genetic diversification, to a two dimensional model in order to study two distinct
parts of the genomes. More specifically, our new model incorporates two biologically meaningful regions of
the genome: promoter regions, and other sites of the genome. The differences between these two regions
are analyzed with regards to the rates of four key processes in these dynamics: gene duplication, gene
loss, gene diversification and horizontal gene transfer (HGT). We apply our model to the data available
from scanning sequenced prokaryote genomes with the aid of sequence searching programs (e.g. BLAST).
Our preliminary results suggest greater stability of mobile promoter dynamics inside the promoter regions
rather than in other genomic regions.
[1 ] Mark WJ van Passel, Harm Nijveen, and Lindi M Wahl. Birth, death, and diversification of mobile
promoters in prokaryotes. Genetics, 197(1):291–299, 2014.
CD4+ T cell count based HIV treatment: effect of initiation timing of ART on HIV
epidemics
S.M.A. Rahman1∗ , N.K. Vaidya2 , X. Zou1
1 Department of Applied Mathematics
University of Western Ontario
2 Department of Mathematics and Statistics
University of Missouri-Kansas City
E-mail:[email protected]
In absence of effective vaccines, pre-exposure prophylaxis (PrEP) and post-exposure prophylaxis (PEP)
demonstrate substantial impact on HIV transmission. Antiretroviral treatment (ART) has the potential
to reduce mortality and disease progression among HIV infected individuals. ART can significantly reduce
the viral load in a body of treated HIV patients thus preventing infections to their partners. Whether the
treatment should begin early or delayed is still under debate. This study addresses the impact of various
ART programs on the HIV epidemic and demonstrates the optimum timing of ART initiation. Our results
show that although ART may not be able to eliminate HIV/AIDS alone, it can significantly contribute to
reduce the overall HIV transmission and prevalence, and alter the current trend of HIV dynamics.
40
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
The Fixation Probability of Budding Viruses with Applications to Influenza A Virus
J. Reid, L. M. Wahl
Department of Applied Mathematics
University of Western Ontario
E-mail: [email protected]
Human viruses can be classified based on their utilization of one of three major egress mechanisms.
The first is lysis of the cell, which results in cellular apoptosis, and thus, cell death. The other two
mechanisms, budding and exocytosis, retain viability of the cells. Budding is a form of egress in which
the virions steal a portion of the cellular membrane to gain a viral envelope. Finally, exocytosis occurs
when virions are packaged in vesicles and transported to the cell membrane, where they fuse and are released. While non-enveloped viruses commonly utilize exocytosis, some enveloped types may also employ it.
When the genomes of viruses are replicated, there is a chance that mutations occur. These mutations can be beneficial, deleterious, or silent, and may affect any property associated with the organism.
Over time, these mutations either become fixed in the growing population of progeny, or become extinct,
based on selective pressures that promote or oppose the mutant population. The fixation of novel mutations is the underlying process by which viruses adapt to environmental pressures such as new antiviral
pharmaceuticals, or in order for them to infect a new host.
To model the population of budding viruses we developed a system of ordinary differential equations,

dF

= −(A + C)F (t) + BM (t),


dt


dI
(3)
= AF (t) − (D + E)I(t),

dt



dM


= EI(t) − DM (t),
dt
where F represents the free viruses that are not attached to a host cell, I represents the cells that are
infected by the virus but not yet in the budding stage, and M represents the mature cells, the infected
cells that are budding free viruses. Parameters A, C, B, E, and D represent the attachment, clearance,
budding, eclipse, and cell death rates. This model was extended to examine gamma-distributed eclipse
times by including a sequence of k infected stages before the budding stage. The parameter values used
are approximated from recent literature on Influenza A virus.
Numerical simulations were used to track the virions throughout a growth phase, followed by a transmission bottleneck as the virus infects a new host. Starting with a wild-type population, beneficial mutations
were introduced, to examine fixation probabilities. Specific examples of the effects of beneficial mutations
are: increasing the attachment, eclipse, or budding rates and reducing the clearance, or cell death rates.
In parallel analytical work, the fixation probabilities are estimated by a probability generating function
that represents the number of free virions in this mutant lineage at any given time.
In summary, the findings will shed light on mechanisms of adaption used by budding viruses of significant importance to human health, in particular the Influenza A virus, when faced with selective pressures.
41
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
On the evolution of seasonal migration
Timothy Reluga
Departments of Mathematics and Biology
Pennsylvania State University
E-mail:[email protected]
Humans have long observed and documented nature’s mass seasonal migrations of vertebrate and
arthropod species with almost mystical fascination. However, the modern theoretical characterization of
the evolution of seasonal migrations has to-date been neglected, in large part due to the complications
– the puzzle is fundamentally one of temporal forcing of a spatially structured population with densitydependent regulation.
In this talk, I will discuss our recent spatially-explicit models of the evolution of seasonal migration,
including necessary conditions for migration, the potential for sympatric speciation, and open conjectures
on the existence of unique stable migratory strategy allocations. I will conclude by arguing that strong
seasonality is the only phenomena that can drive the evolution such farsighted movement behaviors, and
must be a pre-condition for the evolution of intelligent life on every habitable planet in the galaxy.
Modeling HIV treatment and slow CD4+ T cell decline
Libin Rong
Department of Mathematics and Statistics
Oakland University
E-mail:[email protected]
Highly active antiretroviral therapy can effectively control HIV replication in many infected individuals.
Some data suggested that viral decay dynamics may depend on the stages of the viral replication cycle
inhibited by different drugs. In this talk, I will use a mathematical model including multiple infection
stages to study the effect of various drug classes on the viral load dynamics under treatment. The model
will be used to explain the discrepancy of the viral load change observed in patients receiving raltegravir
and efavirenz-based therapy. I will also develop a model on the basis of a new mechanism to explain the
slow time scale of CD4+ T cell decline during chronic HIV infection. Modeling prediction will be compared
with long-term CD4+ T cell data in untreated HIV patients.
42
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Dynamics of the two delays Bélair-Mackey equation and delayed recruitment models with
maximized lifespan
Gergely Röst
Bolyai Institute
University of Szeged
E-mail: [email protected]
We study the dynamics of a differential equation with two delayed terms, representing a positive and a
negative feedback, that was proposed by Bélair and Mackey for mammalian platelet production, and the
same equation arises naturally for three-stages single species populations as well. By combining various
techniques, we prove delay dependent and absolute global stability results for the trivial and for the positive equilibrium, providing new mathematical results as well as novel insights for the related applications.
We show that, somewhat surprisingly, the introduction of a removal term with fixed delay in population
models can simplify and stabilize the otherwise complex dynamics of the equation, and we investigate the
bifurcations created by such terms.
This is a joint work with Alfonso Ruiz-Herrera and Hassan El-Morshedy.
Modeling the Geographic Spread of Rabies in China
Shigui Ruan
Department of Mathematics
University of Miami
E-mail:[email protected]
Recent phylogeographical analyses of rabies virus clades indicate that the human rabies cases in different
and geographically unconnected provinces in China are epidemiologically related. In order to investigate
how the movement of dogs affects the geographically inter-provincial spread of rabies in Mainland China,
we propose a multi-patch model for the transmission dynamics of rabies between dogs and humans, in
which each province is regarded as a patch. In each patch the submodel consists of susceptible, exposed,
infectious, and vaccinated subpopulations of both dogs and humans and describes the spread of rabies
among dogs and from infectious dogs to humans. It is assumed that only the movement of dogs between
patches may spread the disease from patch to patch. The existence of the disease-free equilibrium will
be discussed, the basic reproduction number will be calculated, and the effect of moving rates of dogs
between patches on the basic reproduction number will be studied. To investigate the rabies virus clades
lineages, the two-patch model will be used to simulate the human rabies data to investigate the interprovincial spread of rabies between Guizhou and Guangxi, Hebei and Fujian, and Sichuan and Shaanxi,
respectively. It is found that the basic reproduction number of such a two patch model can be larger than
1 even the isolated basic reproduction numbers of these two patches are less than 1. This indicates that
the immigration of dogs may make the disease endemic even the disease dies out in each isolated patch
when there is no such immigration. Sensitivity analysis of the basic reproduction number implies that
the direction of immigration plays a dominant role in the transmission dynamics and this may be helpful
in identifying priority regions for disease control. In order to reduce and prevent geographical spread of
rabies in China, our results suggest that the management of dog market and trade need to be regulated
and transportation of dogs need to be better monitored and under constant surveillance.
43
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
From local stability to global stability of equilibria
Azmy S. Ackleh, Paul L. Salceanu
Department of Mathematics
University of Louisiana at Lafayette
E-mail:[email protected]
Let X ⊆ Rn , Ξ ⊆ Rm f : X × Ξ → X be a C 1 function. We consider the dynamical system x0 = f (x, ξ),
where “0” represents the derivative when t ∈ R, respectively the next iteration when t ∈ Z. We show
that if Ξ0 ⊂ Ξ is connected, for any ξ ∈ Ξ0 the system has a unique interior equilibrium Eξ , for any
ξ ∈ Ξ0 the interior equilibrium is locally asymptotically stable, and there exists a ξ0 ∈ Ξ0 such that Eξ0
attracts all solutions x(t, x, ξ0 ) with x ∈ X then Eξ attracts all solutions in X, for all ξ ∈ Ξ0 . To show the
applicability of this theory we provide examples ranging from a discrete selection-mutation models to a
discrete juvenile-adult model to a continuous virus dynamics model. The global stability results established
for some of these examples provide substantial improvement of existing results.
Spreading speeds and traveling waves of two species competition systems with nonlocal
dispersal in periodic habitats
Wenxian Shen
Department of Mathematics and Statistics
Auburn University
E-mail: [email protected]
This talk is concerned with spreading speeds and traveling wave solutions of two species competition
systems with nonlocal dispersal in periodic habitats. It first shows the existence and characterization
of spreading speeds in both spatially and temporally periodic habitats. Then it shows the existence,
uniqueness, and stability of periodic traveling wave solutions in spatially periodic habitats.
Is Rotational Harvesting really good?
Junping Shi
Department of Mathematics
College of William and Mary
E-mail: [email protected]
It is a common understanding that rotational cattle grazing provides a better yield than continuous
grazing, but a qualitative analysis is lacking in the agriculture literature. In rotational grazing, cattle
periodically move from one paddock to another in contrast to continuous grazing, in which the cattle graze
on a single plot for the entire grazing season. Here we quantitatively show how production yields and
stockpiled forage are greater in rotational grazing in some harvesting models. We construct a vegetation
grazing model on a fixed area, and by using parameters obtained from agricultural publications and keeping
the minimum value of remaining forage constant, our result shows that both the number of cattle per acre
and stockpiled forage increase for all tested rotational configurations than the continuous grazing. Some
related spatial harvesting models are also discussed. This is a joint work with Mayee Chen (Jamestown
High School).
44
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Plasticity and Cell Division Competition in Colorectal Cancer Development
A. Mahdipour-Shirayeh and S. Sivaloganathan
Biomedical Research Group, Applied Mathematics Department
University of Waterloo
E-mails: amahdipo@uwaterloo, [email protected]
From the viewpoint of mathematical modeling, colorectal cancer has been studied in a wide variety
of recent publications. Although from the perspective of a general mechanism and regulatory system the
situation even for a healthy crypt is still not well-understood, there exists an increasing number of papers
focusing on the hypothesis that disjoint compartments and associated external processes play a crucial role.
In this talk, we consider a new mathematical model for the structure of the human colon and investigate
the role of plasticity and various types of division in the context of two and three compartment models.
One of the compartments includes stem-cells and the other compartment(s) include progenitor and/or fully
differentiated cells. This research is focussed on the key role of asymmetric division compared to plasticity
which in turn may lead to an increase in the number of stem-cells or progenitors. Understanding this
process in normal tissues will help in identifying the cancer development in a crypt when a new mutant
arises in the stem-cell compartment.
Glycolysis & other metabolic pathways in cancers
Siv Sivaloganathan
Department of Applied Mathematics
University of Waterloo
E-mail: [email protected]
Targeting metabolic pathways in malignant tumours shows increasing promise as an effective therapeutic strategy in clinical oncology. Thus, unravelling details of metabolic pathways used by cancer cells,
particularly those pathways that are differentially activated or suppressed in tumours, is of much current
interest. In 1997, Helmlinger et al published “in-vivo” experimental results of pH and pO2 levels as functions of distance from a single blood vessel, on the micrometer scale. We show how these results provide
unique insights into cancer cell metabolism when combined with an appropriate mathematical model.
Structure of fitness distributions in evolutionary dynamics
Matteo Smerlak
Perimeter Institute for Theoretical Physics
E-mail: [email protected]
Darwinian evolution operates on heterogeneous populations (of genes, memes, etc.) under the principle
of the “survival of the fittest”. For large populations this process can be modeled as a flow on the
space of fitness distributions. We identify the attractors of this flow: a one-parameter family of continuous
distributions which generalizes the “traveling fitness waves” found in [Tsimring, Levine, Kessler, Phys. Rev.
Lett., 76(23), 4440-4443 (1996)]. Unlike the latter, our distributions account for both positive and negative
selection, and are consistent with data from (i) genetic algorithms, (ii) Wright-Fisher simulations, and (iii)
empirical fitness distributions for RNA viruses. From a theoretical perspective, our limiting distributions
can be seen as the asymptotic solutions of the “Fisher fundamental theorem” tower of cumulant equations,
whose “dynamical insufficiency” is therefore resolved.
45
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
The viral spread of a zombie media story
Robert Smith?
The Department of Mathematics
The University of Ottawa
E-mail: [email protected]
We use the case study of a popular media story the 2009 coverage of a mathematical model of zombies to
examine the viral-like properties of a story’s propagation through the media. The coverage of the zombie
story is examined and then a model for the spread of a media story is developed. Stability conditions
are derived and the model is refined to include multiple secondary hooks, a series of additional pieces
of information that may reignite an existing story. Sample scenarios are investigated, under a variety
of suboptimal provisions. Conditions under which a story goes viral include initial newsworthiness, the
natural lifespan of the story, durability after the fact and at least one secondary hook that occurs early in
the story’s lifespan.
Mathematical Modelling and Analysis of Tumor-Immune Delayed System
Yasuhiro Takeuchi
Department of Physics and Mathematics
Aoyama Gakuin University
E-mail:[email protected]
In this presentation, we study the dynamical behavior of a tumor-immune system interaction model
with two discrete delays, namely the immune activation delay for effector cells and activation delay for
Helper T cells (HTCs). By analyzing the characteristic equations, we establish the stability of two equilibria
(tumor-free equilibrium and immune-control equilibrium) and the existence of Hopf bifurcations when two
delays are used as the bifurcation parameter. Our results exhibit that both delays do not affect the stability
of tumor-free equilibrium. However, they are able to destabilize the immune-control equilibrium and cause
periodic solutions. We numerically illustrate how these two delays can change the stability region of the
immune-control equilibrium and display the different impacts to the control of tumors. The numerical
simulation results show that the immune activation delay for HTCs can induce heteroclinic cycles to
connect the tumor-free equilibrium and immune-control equilibrium. Furthermore, we observe that the
immune activation delay for HTCs can even stabilize the unstable immune-control equilibrium.
46
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Predator-prey models with distributed delay
Alexandra Teslya
Department of Mathematics & Statistics
McMaster University
E-mail: [email protected]
Rich dynamics have been demonstrated when a discrete time delay is introduced in a simple predatorprey model. For example, Hopf bifurcations and a sequence of period doubling bifurcations that appear
to lead to chaotic dynamics have been observed. In our research we consider two different predator-prey
models: the classical Gause-type predator-prey model and the chemostat predator-prey. In both cases
we explore how different ways of modelling the time between first contact of the predator with the prey
and its eventual conversion to predator biomass affects the possible range of dynamics predicted by the
models. The models we explore are systems of integro-differential equations with delay kernels from various
distributions including the gamma distribution of different orders, the uniform distribution, and the delta
Dirac distribution. We study the models using bifurcation theory taking the mean delay as the main
bifurcation parameter. We use both an analytical approach and a computer computational approach using
the numerical continuation software XPPAUT and DDE-BIFTOOL. We establish general results common
to all the models. Then the differences due to the selection of particular delay kernels are compared. In
particular, the differences in regions of stability of the coexistence equilibrium are considered.
How seasonally varying predation behaviour and climate shifts affect predator-prey cycles
Rebecca C. Tyson
Mathematics & Statistics
University of British Columbia Okanagan
E-mail: [email protected]
While mathematical models have established that predator-prey interactions can drive population cycles, the assumption has always been that the functional response of the predator is an inherent property
of that particular predator-prey interaction, and therefore does not vary substantially. There is evidence
however, that some predators respond to strong seasonal environmental variation with a behavioral shift
from generalist hunting, when many prey species are available, to specialist hunting, when few species are
present. This shift in prey availability is particularly pronounced at northern latitudes, where seasonal
forcing is both very strong and experiencing dramatic shifts through climate change. We are then led to
explore two questions: (1) How does a seasonal change in predation behaviour affect the dynamics of the
prey and predator populations? and (2) How will these dynamics be affected by climate change? Motivated
by experimental data on great horned owl (Bubo virginialis) behaviour from the boreal forest, we use a
novel, periodic predator-prey model to address these questions.
47
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Modeling the Risk and Dynamics of HIV Infection under Conditions of Drugs of Abuse
Naveen K. Vaidya
Department of Mathematics and Statistics
University of Missouri-Kansas City
E-mail:[email protected]
Drugs of abuse lead not only to high HIV transmission, but also to high viral load, increased disease
progression, and severe neuropathogenesis.ÊTo explore effects of drugs of abuse on the risk and dynamics
of HIV infection, I will present mathematical models that agree well with experimental data from simian
immunodeficiency virus infections of morphine-addicted macaques. Using our models, we evaluate the
target cell population switch due to morphine-induced alterations in HIV coreceptor expression. Our results
show that the proportion of target cells with higher susceptibility remains high in morphine conditioning,
resulting in higher viral replications and accelerated disease progressions. Furthermore, we compute the
increased risk of HIV infection due to higher target cell susceptibility in morphine conditioning, and
investigate how this risk is affected by the pharmacodynamics properties of morphine.
Seasonal and Pandemic Influenza
Pauline van den Driessche
Department of Mathematics and Statistics
University of Victoria
E-mail: [email protected]
From data on influenza A outbreaks, it is observed that a pandemic subtype sometimes coexists with the
previous subtype, but sometimes replaces the previous seasonal subtype. For example, the 1977 pandemic
H1N1 subtype co-exists with the seasonal H3N2 subtype, but in 1957 the pandemic subtype H2N2 replaced
the seasonal subtype H1N1. In an attempt to understand conditions for each situation, a hybrid model for
influenza dynamics that incorporates seasonal and pandemic subtypes and cross-immunity is developed.
Using a combination of analytical and numerical techniques, a relation determining replacement is derived
that depends on the basic reproduction numbers of seasonal and pandemic influenza as well as the crossimmunity between the pandemic subtype and any seasonal strain. For intermediate levels of cross-immunity
the pandemic may replace the seasonal subtype; whereas for strong and weak cross-immunity there may
be co-existence. [Joint work with S.M. Asaduzzaman and J. Ma]
Pairwise model for non-Markovian SIR type epidemics on networks
Zsolt Vizi
Bolyai Institute
University of Szeged
E-mail: [email protected]
In this talk, a generalization of pairwise models to non-Markovian epidemics on networks is presented.
For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations, which shows excellent agreement with results based on the explicit stochastic simulations.
The corresponding pairwise reproduction number and an implicit relation between this and the final epidemic size are also shown. The model for arbitrary distribution is an integro-differential equation and the
generalization of analytical results are presented. Furthermore, the impact of non-markovian recovery time
on network epidemics is explored and illustrated by examples from typical distribution families, such as
uniform, gamma and lognormal. This is a joint work with Gergely Röst and Istvan Z. Kiss.
48
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Calculating the basic reproduction numbers for non-homogeneous epidemic models
Jin Wang
Department of Mathematics
University of Tennessee at Chattanooga
E-mail: [email protected]
The basic reproduction number, commonly denoted R0 , is of fundamental importance in epidemic
modeling. Although the threshold dynamics framework associate with R0 has been well established for
autonomous ODE systems characterizing homogeneous environments, the analysis and computation of
R0 for non-homogeneous epidemic models remain difficult in general. In this talk, we discuss the basic
reproduction numbers for time-periodic and spatially heterogeneous epidemic models, representing two
important types of non-homogeneity. We present efficient numerical methods to compute R0 for such
models, and demonstrate the application through non-trivial examples.
Complex alternative stable states in a three dimensional intraguild predation model
Lin Wang
Department of Mathematics and Statistics
University of New Brunswick
E-mail:[email protected]
In this talk, we present a three-species food web model involving intraguild predation. We show
the model undergos bifurcations of equilibria including saddle-node, transcritical and Hopf bifurcations.
Bifurcations of limit cycles including saddle-node, Neimark-Sacker and homoclinic bifurcations have also
been numerically detected. These bifurcations result in very rich dynamics leading to the occurrence of
multi-type bi-stability and tri-stability. The phenomena of multi-stability exhibited in the model suggest
that intraguild predation can promote multiple combinations of alternative stable states. In particular, it
is shown that one stable state is a stable invariant torus. The talk is based on joint work with Drs. Xi Hu
and James Watmough.
Transmission dynamics of avian influenza
Xiang-Sheng Wang
Department of Mathematics
Southeast Missouri State University
E-mail:[email protected]
In this talk, we will investigate the transmission dynamics of avian influenza among migratory birds. A
model incorporating seasonal migration activities and non-monotonic disease transmission process will be
analyzed. If avian influenza is absent, the evolution of bird population is fully determined by a dynamic
threshold that can be explicitly given in terms of model parameters. However, when the epidemiological
impact is taken into consideration, the model dynamics becomes much subtle and is determined by both
ecological and epidemiological dynamic thresholds. Our study sheds a light on the analysis of dynamical
behavior for periodic systems with time delay. This talk is based on a joint work with Professor Jianhong
Wu of York University.
49
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Modelling the fear effect in predator-prey interactions
Xiaoying Wang
Department of Applied Mathematics
Western University
E-mail: [email protected]
A recent field manipulation on a terrestrial vertebrate showed that the fear of predators alone altered
anti-predator defenses to such an extent that it greatly reduced the reproduction of prey. Because fear can
evidently affect the populations of terrestrial vertebrates, we proposed a predator-prey model incorporating
the cost of fear into prey reproduction. Our mathematical analyses show that high levels of fear (or equivalently strong anti-predator responses) can stabilize the predator-prey system by excluding the existence
of periodic solutions. However, relatively low levels of fear can induce multiple limit cycles via subcritical
Hopf bifurcations, leading to a bi-stability phenomenon. Compared to classic predator-prey models which
ignore the cost of fear where Hopf bifurcations are typically supercritical, Hopf bifurcations in our model
can be both supercritical and subcritical by choosing different sets of parameters. We conducted numerical
simulations to explore the relationships between fear effects and other biologically related parameters (e.g.
birth/death rate of adult prey), which further demonstrate the impact that fear can have in predator-prey
interactions. For example, we found that under the conditions of a Hopf bifurcation, an increase in the
level of fear may alter the direction of Hopf bifurcation from supercritical to subcritical when the birth
rate of prey increases accordingly. Our simulations also show that the prey is less sensitive in perceiving
predation risk with increasing birth rate of prey or increasing death rate of predators, but demonstrate
that animals will mount stronger anti-predator defenses as the attack rate of predators increases.
Virulence evolution of a parasite infecting male and female hosts
Alison Wardlaw and A. F. Agrawal
Department of Ecology and Evolutionary Biology
University of Toronto
[email protected]
Parasites experience different tradeoffs between transmission and virulence in male and female hosts if
the sexes vary in life history or disease-related traits. A pathogen infecting two host types could adapt by
facultatively expressing sex-specific exploitation rates, or, if constrained to express the same exploitation
rate in each sex, compromise between the ideal trait in each. We model both scenarios, using invasion
analyses to find the evolutionarily stable strategy of a horizontally transmitted parasite. We incorporate
differences between the sexes in susceptibility and resistance to disease and vary the contact pattern
between and among sexes. We found that when there is differential susceptibility and resistance to disease,
the evolutionarily stable exploitation rate of a constrained parasite changes with contact pattern. As the
amount of within sex transmission increases, the ESS shifts closer to the optimum trait value in the more
susceptible sex, which has a higher reproductive value for the pathogen. The sex-specific exploitation rates
of a facultative parasite do not change with contact pattern. An unconstrained parasite always evolves to
express the same trait value in each sex as it would in a homogeneous host population composed entirely
of that sex. However, if we allow for vertical transmission from mother to offspring, the exploitation rate
expressed in females (but not males) changes with contact pattern because females are more valuable hosts.
We conclude that differences in contact pattern and susceptibility to disease play an important role in the
ESS determination of a constrained parasite when the sexes also differ in resistance and of an unconstrained
parasite when there is vertical transmission.
50
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Successional genetics of incipient ring species complexes:
isolation by distance and adaptations
Michael Williamson1,2 and Cortland Griswold1
1 University of Guelph
2 Queen’s University
E-mail: [email protected]
Ring species form when two colonization fronts diverge evolutionarily around a geographical barrier.
Reproductive isolation exists between the populations at the colonization fronts upon secondary contact.
Gene flow between the two terminal populations exists via dispersal between populations around the base of
the ring. Here, a model of ring species formation is proposed that considers intraspecific succession patterns.
There is a three-phase succession dynamic; a leading colonization wave consisting of a high dispersing,
sub-optimally adapted ecomorph, replaced by a second wave consisting of high dispersing, locally-adapted
ecomorphs and a third wave of low dispersing locally-adapted ecomorphs. Ecomorph identity is determined
by three-loci genotypes. Two loci code for local adaptation and experience negative reciprocal sign-epistatic
interactions. The third locus codes for dispersal where the high dispersal allele experiences a negative
epistatic interaction with the local adaptation alleles. The model gives insight into the transient dynamics of
ring-species formation and the ecological and genetic conditions leading to a stable versus unstable ring for
genetic architectures involving two local adaptation loci. Reproductive isolation does not immediately form
between the two terminal populations. Instead, a Lotka-Volterra competition-mediated successional process
drives the formation of postzygotic reproductive isolation between the terminal populations. Isolation is
due to both environmental- and developmental-mediated barriers. More broadly, the model analyzes the
formation of two distinct clines connecting reproductively-distinct populations. The terminal contact cline
is abrupt, limiting gene flow while the ancestral contact cline is gradual and more permeable to gene flow.
The effects of asymmetrical gene flow on ring complex shape are analyzed by numerically approximating
terminal contact zone bifurcations and equilibrium behavior for various genetic and ecological asymmetry
drivers.
Sensitivity of the General Rosenzweig–MacArthur Model to the Mathematical Form of the
Functional Response: a Bifurcation Theory Approach
Gail S. K. Wolkowicz
Department of Mathematics and Statistics
McMaster University
E-mail:[email protected]
The equations in the Rosenzweig–MacArthur predator-prey model have been shown to be sensitive to
the mathematical form used to model the predator response function even if the forms used have the same
basic shape: zero at zero, monotone increasing, concave down, and saturating. Here, we revisit this model
to help explain this sensitivity in the case of Holling type II, Ivlev, and Trigonometric response functions.
We consider both the local and global dynamics and determine the possible bifurcations with respect to
variation of the carrying capacity of the prey, a measure of the enrichment of the environment. We give
an analytic expression that determines the criticality of the Andronov-Hopf bifurcation, and prove that
although all three forms can give rise to supercritical Andronov-Hopf bifurcations, only the Trigonometric
form can also give rise to subcritical Andronov-Hopf bifurcation and has a saddle node bifurcation of
periodic orbits giving rise to two coexisitng limit cycles, providing a counterexample to a conjecture of
Kooij and Zegeling (1996) and a related result in a paper by Attili and Mallak (2006). We also revisit the
ranking of the functional responses, according to their potential to destabilize the dynamics of the model
and show that given data, not only the choice of the functional form, but the choice of the number or
position of the data points can influence the dynamics predicted.
This is joint work with Gunog Seo of Colgate University.
51
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Coexistence and competitive exclusion in an SIS model with standard incidence and
diffusion
Yixiang Wu
Department of Applied Mathematics
Western University
E-mail:[email protected]
In this talk, I present a two strain SIS model with diffusion, spatially heterogeneous coefficients of the
reaction part and distinct diffusion rates of the separate epidemiological classes. First, it is established
that the model with spatially homogeneous coefficients leads to competitive exclusion and no coexistence
is possible in this case. Then it is proved that if the invasion number of strain j is larger than one, then
the equilibrium of strain i is unstable; if, on the other hand, the invasion number of strain j is smaller
than one, then the equilibrium of strain i is neutrally stable. In the case when all diffusion rates are equal,
global results on competitive exclusion and coexistence of the strains are established. Finally, evolution of
dispersal scenario is considered and it is shown that the equilibrium of the strain with the larger diffusion
rate is unstable. Simulations suggest that in this case the equilibrium of the strain with the smaller diffusion
rate is stable.
Evolution of mobility in predator-prey systems
Fei Xu, Ross Cressman and Vlastimil Křivan
Department of Mathematics
Wilfrid Laurier University
E-mail:[email protected]
We investigate the dynamics of a predator-prey system with the assumption that both prey and predators use game theory-based strategies to maximize their per capita population growth rates. The predators
adjust their strategies in order to catch more prey per unit time, while the prey, on the other hand, adjust
their reactions to minimize the chances of being caught. We assume each individual is either mobile or
sessile and investigate the evolution of mobility for each species in the predator-prey system. When the
underlying population dynamics is of the Lotka-Volterra type, we show that strategies evolve to the equilibrium predicted by evolutionary game theory and that population sizes approach their corresponding stable
equilibrium (i.e. strategy and population effects can be analyzed separately). This is no longer the case
when population dynamics is based on the Holling II functional response, although the strategic analysis
still provides a valuable intuition into the long term outcome. Numerical simulation results indicate that,
for some parameter values, the system has chaotic behavior. Our investigation reveals the relationship
between the game theory-based reactions of prey and predators, and their population changes.
52
ICMA-V, October 2-4, 2015
Abstracts II-2——Talks
Temperature-driven model for the abundance of Culex mosquitoes
Don Yu
Department of Mathematics and Statistics
York University
Email: [email protected]
Vector-borne diseases account for more than 17% of all infectious diseases worldwide and cause more
than 1 million deaths annually. Understanding the relationship between environmental factors and their
influence on vector biology is imperative in the fight against vector-borne diseases such as dengue and West
Nile virus. We develop a temperature-driven abundance model for West Nile vector species, Culex pipiens
and Culex restuans. Temperature dependent response functions for mosquito development, mortality,
and diapause were formulated based on results from published field and laboratory studies. Preliminary
results of model simulations compared to observed mosquito traps counts from 2004-2014 demonstrate the
capacity of our model to predict the observed variability of the mosquito population in the Peel Region of
southern Ontario over a single season. The proposed model has potential to be used as a real-time mosquito
abundance forecasting tool and would have direct application in mosquito control programs. This is a work
supported by CIHR, PHAC and NSERC, under the supervision of Professors Neal Madras and Huaiping
Zhu.
Dynamics of an HIV virotherapy model with nonlinear incidence and two delays
Yuan Yuan
Department of Mathematics and Statistics
Memorial University of Newfoundland
E-mail:[email protected]
In this talk, we propose a mathematical model for HIV infection with delays in cell infection and virus
production. The model examines a viral-therapy for controlling infections through recombining HIV virus
with a genetically modified virus. For this model, we derive two biologically insightful quantities (reproduction numbers) R0 and Rz , and their threshold properties are discussed. When R0 < 1, the infection-free
equilibrium E0 is globally asymptotically stable. If R0 > 1 and Rz < 1, the single-infection equilibrium
Es is globally asymptotically stable. When Rz > 1, there occurs the double-infection equilibrium Ed , and
there exists a constant Rb such that Ed is asymptotically stable if 1 < Rz < Rb . Some simulations are
performed to support and complement the theoretical results.
This is a joint work with Dr. Yun Tian.
53
ICMA-V, October 2-4, 2015
Abstracts II-3—— Posters
Mechanisms underlying the generation of disease recurrence
Wenjing Zhang
Department of Mathematics and Statistics
York University
E-mail:[email protected]
In this talk, we discuss the appearance of recurrent infection, that is, the cycles consisting of long periods
close to the disease free equilibrium, punctuated by brief bursts of disease. This pattern of recurrence occurs
in many diseases, including the intriguing pattern of “viral blips” in HIV, as well as the recurrent episodes
characteristic of autoimmune diseases, such as multiple sclerosis, multifocal osteomyelitis, lupus, eczema,
and psoriasis. We will study several mechanisms which underly these physiologically relevant patterns of
infection. Our analysis shows that when the incidence function is convex, bistable equilibrium solutions,
Hopf and generalized Hopf bifurcations and, in particular, homoclinic bifurcations may all contribute to
disease recurrence.
This is a joint work with Dr. Lindi M.Wahl and Dr. Pei Yu.
Basic Reproduction Ratios for Periodic Compartmental Models with Time Delay
Xiaoqiang Zhao
Department of Mathematics and Statistics
Memorial University of Newfoundland
E-mail:[email protected]
In this talk, I will report our recent research on time-delayed compartmental population models in a
periodic environment. We establish the theory of basic reproduction ratio R0 for such a class of systems. It
is proved that R0 serves as a threshold value for the stability of the zero solution of the associated periodic
linear systems. As an illustrative example, we also apply the developed theory to a periodic SEIR model
with an incubation period and obtain a threshold result on its global dynamics in terms of R0 . If time
permits, I will mention more applications of this theory and the numerical computation of R0 .
54
ICMA-V, October 2-4, 2015
Abstracts II-3—— Posters
Matrix Population Model for Polar Bears Affected by Environmental Changes
N. Bastow, X. Zou
Department of Applied Mathematics
University of Western Ontario
E-mail: [email protected]
Polar bears are top predators in the Arctic that depend on sea ice for all major aspects of survival,
including breeding, hunting and travelling. With the climate in the Arctic warming steadily, the abundance
of sea ice available for Polar bears is decreasing. This results in a loss of habitat, which is predicted to
have a significant impact on Polar Bear survival. Hudson’s Bay is the southern most point in the Arctic
and one of the first to show such visible signs of climate changes. Due to this, focus will be concentrated
on the Polar bear population located in this region.
To model the population of polar bears, a size-classified matrix model was adapted from the life cycle
graph given by Hunter et al [1]. The model is given by
N (t + 1) = A(t)N (t)
(4)
where A(t) is the population projection matrix from time t to t + 1 and the entries of the matrix include
survival, breeding probability and the number of cubs in successful litters. Each parameter was time dependent such that it decreased in time. This was done to model the negative impact of the yearly increases
in temperature. The rate at which each parameter decreased with time was varied to look at three cases.
The first case was when only survival was effected and other parameters remained constant. The second
case was when both survival and breeding were effected. The final case looked at when all parameters
were affected differently depending on the stage (ie. Juveniles are impacted by change more than Prime
Adults).
Numerical analysis was done on the model for each case using parameter values calculated from data
found by Regehr et al [2]. Sensitivity and elasticity analysis was used to determine which parameter most
affected the population growth rate, λ. Further analysis looked for a critical point where λ was determined
by male survival only, resulting in unstable growth and population collapse.
In conclusion, the results found by the model will communicate the importance that environment
changes have on biological systems. The impact of climate change on Polar bears is significant and interventions should be made to stop or slow down the population declines.
[1 ] Hunter, C., Hal, C., Runge, M., Regehr, E., Amstrup, S., & Stirling, I. (n.d.). Polar Bears in the
Southern Beaufort Sea II: Demography and Population Growth in Relation to Sea Ice Conditions .
Retrieved December 15, 2014, from
http : //www.usgs.gov/newsroom/special/polar bears/docs/U SGS P olarBear Hunter SB−II Demography.pdf
[2 ] Regehr, E., Lunn, N., Amstrup, S., & Stirling, I. (2007). Effects Of Earlier Sea Ice Breakup On Survival
And Population Size Of Polar Bears In Western Hudson Bay . Journal of Wildlife Management,71(8), 26732683.doi:10.2193/2006-180.
55
ICMA-V, October 2-4, 2015
Abstracts II-3—— Posters
A Bayesian approach to include individual development variation in life cycle models
Marı́a Soledad Castaño1,2,∗ , Helene Guis1 , Jean Vaillant3 , Thomas Balenghien1 , Xavier Allene1 , Ignace
Rakotoarivony1 , David Pleydell1,2,∗ .
1 CIRAD, UMR-1309 CMAEE, TA-A15/G, Campus International de Baillarguet
2 INRA, UMR-1351 CMAEE, Domaine Duclos, Prise D’eau
3 LAMIA (EA4540), Universit des Antilles-Guyane
E-mail:[email protected]
Matrix models are popular tools for describing processes and dynamics of arthropod populations. A
popular approach is to build stage structured models that ignore within-stage variation in the developmental status of individuals, a strong assumption that can compromise precision. For many arthropod life
cycles, non-geometric distributions of maturation times are typically observed in laboratory studies. Moreover, there is typically a minimum maturation time that represents the most rapid development within a
stage. It is known that when reproducing maturation times with a model, including or not within-stage
variability determines respectively whether or not a minimum maturation time or a geometric distribution
is obtained. Obviously, the former is a more realistic representation.
It is natural to inquire if and when including individual variability improves model fit. The approach
presented here attempts, at least in part, to address this question. For that, a discretised integral projection model is included within each stage of a stage structured matrix population model. This basically
augments the resolution of the modelled developmental process and introduces an associated kernel. Temperature is used as an environmental covariable, though the model could be extended to include other
climatic/environmental variables. Kernel parameters are estimated using Culicoides (a genus of biting
midges) life cycle data from various published and unpublished laboratory studies.
We obtain Bayesian estimates of development kernel parameters at different temperatures using Markov
chain Monte Carlo techniques. We investigate several levels of resolution in the developmental process with
the aim of obtaining a compromise between improved model fit and computational cost. Preliminary results
indicate that extrapolation of kernel parameters to unmeasured temperatures might be least erroneous in
situations where developmental data are available at many points across a large range of fixed experimental
temperatures. Furthermore, we discuss the effects of resolution on posterior estimates of the population
growth rate under different fixed temperatures. Implications for modelling insect phenology and potential
model improvements are discussed.
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ICMA-V, October 2-4, 2015
Abstracts II-3—— Posters
Modeling Effects of Drugs of Abuse on HIV-Specific Antibody Responses
Jones M. Mutua, Anil Kumar, Naveen K. Vaidya
Department of Mathematics and Statistics
University of Missouri - Kansas City
E-mail: [email protected]
Drugs of abuse enhance HIV replication and diminish host immune responses. Here, we present a
mathematical model that helps quantify the effects of drugs of abuse on altering HIV-specific antibody
responses. Our model is consistent with the experimental data from simian immunodeficiency virus infection of morphine-addicted macaques. Using our model, we show how altered antibody responses due to
drugs of abuse affect viral infection and clearance, viral load, CD4+ T cells count, and CD4+ T cells loss
in HIV-infected drug abusers.
The boosted sterile insect technique: a powerful new tool for vector control?
David Pleydell1,2 and Jeremy Bouyer2,3
1 INRA, UMR 1309 CMAEE,
2 CIRAD, UMR CMAEE,
3 Laboratoire National dElevage et de Recherches Vtrinaires, Institut Sngalais de Recherches Agricoles
E-mail: [email protected]
The sterile insect technique (SIT) [3] and the auto-dissemination technique (ADT) [2] are amongst
the most powerful methods for insect vector control. These techniques reduce the reproductive success
of target insects by exploiting sexual competition between sterile and natural males (SIT) or by using
wild-type females to disseminate juvenile hormone analogues (JHA) to larval sites (ADT). A combined
“boosted” SIT, where sterile males transfer JHA to females who in turn contaminate larval sites, has been
proposed [1]. Intuitively, large reductions in the economic and ecological costs of insect control are possible.
We attempt to predict the potential efficiency gain and identify key parameters that affect it. A nonlinear system of ordinary differential equations representing the life cycle of the mosquito Aedes albopictus,
sexual competition with sterile males and an accumulation of JHA at larval sites is presented. Parameters
were obtained from the literature and the model was analysed using analytical and numerical techniques.
With no control the system has stationary points at carrying capacity (stable) and eradication (unstable).
Constant release of sterile males decreases the stable equilibrium, increases the unstable equilibrium and
makes eradication a stable equilibrium. A bifurcation occurs when the stable and unstable equilibrium meet
and release rates beyond this threshold guarantee eradication. Dusting sterile males with JHA profoundly
affects the system’s dynamics: the bifurcation is obtained with release rates reduced by a factor of four;
the time to eradication is greatly reduced, particularly for low release rates; the minimum number of
released males required to achieve “eradication” is at least halved. These results are highly sensitive to
small changes in parameters related to JHA transfer, suggesting further laboratory and field trials could
help reduce uncertainties associated with model predictions.
[1 ] Bouyer, Jérémy and Lefrançois, Thierry, Boosting the sterile insect technique to control mosquitoes,
Trends in Parasitology 30, pp. 271-273 (2014).
[2 ] Devine, Gregor J and Perea, Elvira Zamora and Killeen, Gerry F and Stancil, Jeffrey D and Clark,
Suzanne J and Morrison, Amy C, Using adult mosquitoes to transfer insecticides to Aedes aegypti
larval habitats, PNAS 106, pp. 11530-11534 (2009).
[3 ] Dicko, Ahmadou. H. and Lancelot, Renaud. and Seck, Momar. T. and Guerrini, Laure and Sall,
Baba. and Lo,Mbargou. and Vreysen, Marc. J. B. and Lefranois, T. and Fonta, William. M. and
Peck, Steven. L. and Bouyer, Jérémy., Using species distribution models to optimize vector control
in the framework of the tsetse eradication campaign in Senegal, PNAS 111, pp. 10149-10154 (2014).
57
ICMA-V, October 2-4, 2015
Abstracts II-3—— Posters
Dynamics of neural systems with discrete and distributed time delays
B. Rahman, Y.N. Kyrychko, K.B Blyuss
Department of Mathematics
University of Sussex
E-mail:[email protected]
In real-world systems, interactions between elements do not happen instantaneously due to the time
required for a signal to propagate, reaction times of individual elements, and so forth. Moreover, time
delays are normally non-constant and may vary with time. This means that it is vital to introduce
time delays in any realistic model of neural networks. In order to analyse the fundamental properties
of neural networks with time-delayed connections, we consider a system of two coupled two-dimensional
nonlinear delay differential equations. This model represents a neural network, where one subsystem
receives a delayed input from another subsystem. An exciting feature of the model under consideration is
the combination of both discrete and distributed delays, where distributed time delays represent the neural
feedback between the two subsystems, and the discrete delays describe the neural interaction within each of
the two subsystems. Stability properties are investigated for different commonly used distribution kernels,
and the results are compared to the corresponding results on stability for networks with no distributed
delays. It is shown how approximations of the boundary of stability region of a trivial equilibrium can
be obtained analytically for the cases of delta, uniform and weak gamma delay distributions. Numerical
techniques are used to investigate stability properties of the fully nonlinear system and they fully confirm
all analytical findings.
Large industrial broiler farms can eliminate Marek’s disease by shortening cohort duration
Carly Rozins
Department of Mathematics and Statistics
Queen’s University
E-mail:[email protected]
Marek’s disease is an economically important disease of poultry. The disease is transmitted indirectly,
enabling the spread of disease between cohorts of chickens who have never come into physical contact. We
develop a model which allows us to track the transmission of disease within a barn and between subsequent
cohorts of chickens occupying the barn. It is described by a system of impulsive differential equations. We
determine the conditions that lead to disease eradication. For a given level of transmission we find that
disease eradication is possible if the cohort length is short enough and/or the cohort size is small enough.
Marek’s disease can also be eradicated from a farm if the cleaning effort between cohorts is large enough.
Importantly complete cleaning is not required for eradication and the threshold cleaning effort needed
declines as both cohort duration and size decrease.
58
ICMA-V, October 2-4, 2015
Abstracts II-3—— Posters
Population dynamics for stray cats
Jeff Sharpe
Department of Mathematics
University of Central Florida
E-mail:[email protected]
We formulate and analyze a mathematical model that describes the population dynamics of stray cats.
The model includes three categories: kittens, adult female and adult males. Kittens are born at a rate
proportional to the adult female population. Adults compete both with members of their own sex and
members of the opposite sex for resources. A net reproduction number R0 is defined. If R0 < 1, then the
population goes extinct. If R0 > 1, then the population can persist at a positive and locally asymptotically
stable equilibrium. Possible extensions to the model include the movement of adult males in a spatial
habitat and the spread of feline leukemia. These extensions will be mentioned. The results presented here
represent joint work with A. Nevai.
Modelling HIV virulence evolution in the face of antiretroviral drugs
David R.M. Smith & Nicole Mideo
Department of Ecology & Evolutionary Biology
University of Toronto
E-mail: [email protected]
Antiretroviral drugs, in addition to treating those infected with HIV, are now being used to prevent
HIV acquisition in some uninfected hosts. While effective, it remains unknown if and how this prevention
strategy will influence viral evolution, including key traits like virulence. In HIV, virulence evolution is
constrained by a trade-off: within-host viral load relates positively to infection transmissibility, but also
limits infection duration by accelerating progression to AIDS. Accordingly, viral genotypes that favour
intermediate viral load - and consequently intermediate virulence - have the greatest lifetime transmission
success. Here, we use adaptive dynamics to explore how drug treatments affect this phenomenological
trade-off in a modified Susceptible-Infected compartmental model of ordinary differential equations. We
find that drugs select for increased virulence when used to treat infected hosts, and select for greatest
virulence when used for both prevention and treatment. While drugs will continue to reduce disease
prevalence, monitoring any resulting virulence evolution will remain a priority in order to deduce whether
the epidemiological benefits of these drugs will outpace their evolutionary consequences.
59
ICMA-V, October 2-4, 2015
Abstracts II-3—— Posters
Global Dynamics of Three Species Omnivory Models with Lotka-Volterra Interaction
Ting-Hui Yang
Department of Mathematics
Tamkang university
E-mail:[email protected]
In this work, we consider the community of three species food web model with Lotka-Volterra type
predator-prey interaction. In the absence of other species, each species follows the traditional logistical
growth model and the top predator is an omnivore which is defined as feeding on the other two species. It
can be seen as a model with one basal resource and two gen- eralist predators, and pairwise interactions
of all species are predator-prey type. It is well known that the omnivory module blends the attributes of
several well-studied community modules, such as food chains (food chain models), exploitative competition
(two predators-one prey models), and ap- parent competition (one predator-two preys models). In the sense
of one predator-two preys models, we assume that the prey is inferior than the medium intraguild prey on
apparent competition. Based on this biological restriction, we completely classify all parameters and show
its corresponding global dynamics.
Temperature-driven model for the abundance of Culex mosquitoes
Don Yu
Department of Mathematics and Statistics
York University
Email: [email protected]
Vector-borne diseases account for more than 17% of all infectious diseases worldwide and cause more
than 1 million deaths annually. Understanding the relationship between environmental factors and their
influence on vector biology is imperative in the fight against vector-borne diseases such as dengue and West
Nile virus. We develop a temperature-driven abundance model for West Nile vector species, Culex pipiens
and Culex restuans. Temperature dependent response functions for mosquito development, mortality,
and diapause were formulated based on results from published field and laboratory studies. Preliminary
results of model simulations compared to observed mosquito traps counts from 2004-2014 demonstrate the
capacity of our model to predict the observed variability of the mosquito population in the Peel Region of
southern Ontario over a single season. The proposed model has potential to be used as a real-time mosquito
abundance forecasting tool and would have direct application in mosquito control programs. This is a work
supported by CIHR, PHAC and NSERC, under the supervision of Professors Neal Madras and Huaiping
Zhu.
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ICMA-V, October 2-4, 2015
Campus Map-1
• Three ovals indicate the three buildings involved:, Middlesex College (MC), Physics and Astronomy
(PA) and Social Science Center.
• UWO offers free weekend parking in some selected parking lots, and the three rectangles are such
parking lots with reasonable walking to the three buildings.
• If drive to campus on Friday, you have to pay for parking, either at those attended parking lots or
use coins to get in those un-attended parking lots.
• The arrowed road shows the way coming from the two hotels (Spencer, Guest House)
61
ICMA-V, October 2-4, 2015
Campus Map-2
For your convenience, here is a full map of the campus.
Stiller
Centre
THE RESEARCH PARK
London Campus
999
Collip
Windermere
Manor
COLLIP
Mogenson
Building
250 Metres
CIRCLE
Walking Time: 3-4 Minutes
National
Research
Centre
WINDERMER E ROAD
Spencer Hall
Lambton
Hall
Westminster
Hall
Ausable
Hall
P
Bayfield
Hall
Beaver
Hall
Eight Level
Parkade
Advanced Facility
for Avian Research Support Services
Western Centre for
Health and Family Medicine
London Health
SaugeenMaitland
Graphic
Services
Mount Health Centre
Perth
Drive
Complex
Siebens Sciences Centre Lot University Campus
Support
Services
Chemistry
Lot
West Valley
Building
Dental
Siebens
Sciences
Centre
DR
RT
H
iv
er
Medway
Lot
TOWER LN
N
TER
UNIVERSITY DR
DRIVE
SUNSET
es
Elgin
Lot
SARNIA ROAD
University
Child Care
Centre
Ontario
Hall
Essex
Hall
Sydenham
Hall
N
DR
m
Western Student
Recreation
Centre
PHILIP AZIZ AVE
RO
Thompson
Recreation &
Athletic Centre
HU
Elborn
College
Outdoor
Rink
Emergency Phone
Soccer Pitches
Alumni
Field
Mustangs
Field
OR
TH
W
Student housing
Off-campus buildings
housing Western facilities
AV
E
See detailed parking maps for additional visitor
parking at meters and pay & display areas.
P
Townhouses
(3)
EP
Platt's Lane
Estates
Visitor parking lot
ter's
t. Pe y
To Sminar
T
Se
OS
LO
P
TD
Stadium
Althouse
Lot
Monsignor
Wemple
Hallll
King’s Alumni
Court
Welcome to Western
TER
WA
Perth
Hall
Alumni
House
King's University College
Huron Flats
Lot
London
Hall
Medway
Hall
Practice
Field
South
Barrier-free (accessible) meters
Althouse
Faculty of
Education
RTH
EPWOVE
A
Elgin Hall
WES
South Valley
Lot
ity
To
Univers
King’sge at
Colle ern
West
r’s
Alumni Western & St. Pete
ry
Centre (BMO)
Semina
PE
D
OR
Y 4)
(HW
OX
F
EET
STR
DL E S E X
ROA
D
ND
MO
RICH
MID
Robarts
Res. Inst.
Chemistry
ELG
IN
Health Taylor
Med. Sci
DR
Materials
Sci. Library
Lot
Science Addit.
Visual
Medical
Addit.
Rix
Social
Arts
HURON UNIVERSITY
Natural Biol. Biotron
Clinical Sci. Bio
Science
Lot
Sci. & Geol. GreenLab
Hellmuth COLLEGE
Lot P
Skills
Henderson
Kresge
Hall
Broughdale
Sci.
House
houses
Labatt
House
Young
McIntosh
Visual Arts
Social Science
O’Neill/
Collip
House
Gallery
Centre
South
Ridley
University
Physics
&
Hall
Residence Community
BURNLEA WALK
North
Astronomy Western
Centre
Stevenson
Campus
Science
Huron
Huron College
Hall
Western
Building
Middlesex
Centre
Dining
Lot
Student
P
College
Lawson University
Hall
Services
Weldon
College
Hall
Staging
Library
Springett
Somerville
Lot
House
P
BRESCIA UNIVERSITY
3M
Weldon
Ursuline
Centre
Lot
COLLEGE
Hall
Arts & International &
Law
Brescia
Delaware
Thames
Humanities Graduate Affairs
LAMB
Building
Hall
Building
Hall
TON
DR
LA Building
Talbot
R
MB
College
T
ON
Clare
Music
Spencer Cronyn
Talbot
Alumni
Hall
Building
Obs.
D
Lot
Engineering
R
Hall Heating
Alumni/
Plant
Richard Ivey
MacKay- Thompson
Tennis
Building
Mother
Lassonde Lot
Courts
Pavillion P
St. James
Labatt
Mary
Memorial Building
Health
Manor
Practice
Thompson
Wind
Sci.
Bldg.
Field
a
Tunnel Engineering
North
Th
Lot
Labatt
Hall
Dante
Lenardon
Darryl J. King
Hall
Student Life
Faculty
Cardinal Centre
Building
Carter
The Annex Library
Broughdale
Hall
Services
Building
International House
For a broad selection of parking and other campus maps
visit geography.uwo.ca/campusmaps/
Barrier-free parking is available in all lots.
© 2015. The Cartographic Section, Dept. of Geography, Western.
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ICMA-V, October 2-4, 2015
Participants-1
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ICMA-V, October 2-4, 2015
Participants-2
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ICMA-V, October 2-4, 2015
Participants-3