Using GIS and CA to model
the propagation of infectious
Diseases
Joana Margarida
http://www.artificial-life.com/index.php
"Everything should be made as simple as possible, but not simpler." A. Einstein
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
This study covers several fields:
Study and modelling of diffusion processes
Spatial Epidemiology
Cellular automata (CA)
Link between GIS and CA models
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Diffusion study
•Concerns
how fast and to what extent things grow, transfer and
diffuse. (Banks, R. B., 1994)
•
•The
question is not why the processes take place, but the
methodology involved in utilizing various frameworks for the
analysis and display of data and how the resulting information can be
used to
•Interpret
and predict
•Mathematical
framework:
•
N - magnitude of a growthing quantity
t - time
• x -space direction
• a - intrinsic growth coefficient
•D - diffusion coefficient
•
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Spatial Diffusion
•Propagation
phenomena in time and space of a simple or complex
element (Dauphiné, A, 1995)
•Macrodiffusion
•Diffusion
and Microdiffusion
processes:
contiguity without •Trought new hierarquies
•
constraints
•By
•Particle
•With
•
risk
•Molecular
•
Models: diffusion is represented by elements displacement*
•Aggregation Models
•Particle Models
•DLA and DBM
•Dauphiné­Ottavi
•Percolation Models
•Cellular Automata
•* Brownian movement
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Spatial Diffusion (cont.)
(Cliff, A.D. ET AL, 1981)
•Relocation
•Spatial
Diffusion
Diffusion
•Contagious
•Expansion
Diffusion
Diffusion
•Hierarquical
Diffusion
http://www.spatial.maine.edu/ax/KEH_il
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Spatial Diffusion (cont.)
a)
b)
http://www.nczooeletrack.org/elephants/loomis_maps/
Examples: a) spread of a wildfire, adoption of herbicides, b) migration, oxygen
transfer across a water surface,...
•Why
Study Epidemics?
•Epidemics
repeat themselves in time and space and so provide one data set
upon wich calibrate the model and another data set upon wich test it.
•Models of the spread of infectious diseases should be useful generally in the
analysis of innovation and cultural diffusion patterns. (Cliff, A.D., ET AL,
1981)
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Spatial Epidemiology
Analysis of the spatial/geographical distribution of the incidence of a disease
(Lawson, A. B., 2001)
•Disease
•Statistical
•Epidemiological
approach
models
•Deterministic
•CA
approach
mapping
•Ecological
•Disease
approach
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
analysis
clustering
Statistical Approach
Disease mapping - concerns the use of models to describe the overall
disease distribution on the map (clean the map of extra noise).
Ecological analysis -analysis of the relation between the spatial
distribution of disease incidence and measured explanatory factors.
Disease clustering -analysis of unusual aggregations of disease, assessing
wether there are any areas of elevated incidence of disease within a map
(general and especific clustering)
Incidence of Salmonellosis
http://www.gisca.adelaide.edu.au/~cwright/graddip/communicable_diseases.html
WHO
http://www.who.int/csr/mapping/
What about infectious diseases????
it is assumed that spatial and temporal clustering can be modelled
explicity via a form of contact probability field wich will lead to clustering
in space-time (purely descriptive models for spatial clusters of disease)
(Lawson, A.B, 2001).
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Statistical Approach (cont.)
Point based models and Count based models
Poisson Process
Discrete Binomial distribution for a Poisson Process
http://www.mathworld.wolfram.com/PoissonDistribution.html
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Statistical Approach (cont.)
Likelihood-based approach and Bayesian approach
The probability density of a vector random variable x, depends on a paremeter vector
È as P(x|È). When a realisation of x is observed, we assume that a likelihood can be
defined for the parameter vector.
Likelihood-based approach: values of parameters are based on the likelihood itself
Bayesian approach: values of parameters are assumed to be governed by prior
distributions.
Bayesian approach incorporates random effects wich can describe unobserved
features of the data: population strata random effects, region specific random
effects, individual case random effects,...
Effects peculiar to spatial problems: spatial correlated heteregoneity (analysis of
spatial correlation) and random-object effects (stochastic geometry).
Methods to incorporate autocorrelation in spatial data: krigging autoregressive
(SAR) or conditional autoregressive models (CAR), Markov Random field
models.
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Deterministic Approach
•Mathematical
•Epidemics
models that lead to differential equations
model in a closed population
•r
-infection rate
removal rate
•ñ=¾/r (threshold value) S0>ñ
•¾ -
(Banks, R. B., 1994, Burghes, D.N. ET AL, 1981)
•SI
model for microparasites (G.A. DE LEO, A.P.
Dodson)
•http://hilbert.dartmouth.edu/~m4w02/syl2.htm
Threshold Theorem of Epidemiology - When (S0 -ñ) is small compared to ñ, then the number of individuals
who ultimately contract the disease is aproximately 2(S0 ­ñ)
O D E's - assume there is an homogeneous mixing of types, in space.
To study the geographical spread of epidemics:
PD E's
N=N(x,y,z,t)
Still treat the population as continuous entity, and neglect the fact that populations are
composed of single interacting individuals!! (Fuk´s, H. ET AL)
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Epidemiological Data -Types:
Point Data
Count Data
•Tricky!!
•-generally
•-excessive detail that can be useless
•-confidentiality
•- ecological fallacy (P. Elliot ET AL,
data
•-aggregation increases the local sample size
and avoids the need to use exact addresses
•-Smoothing involved in counts yeld an
invariance at regional level and disjunction
between risk and location.
•- ecological fallacy (P. Elliot ET AL, 2000)
2000)
an aggregation of case event
•If
there is case event data that should be used, and it is not recommended the
lost of information by aggregation! (P. Elliot ET AL, 2000)
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Epidemiological Data -Sources:
•Health Data and Population Data (Relative Risk Assessment)
Health Data
statutory registration systems ­death (errors), and infectious diseases recording (incomplete).
administrative systems (hospitals, admissions, prescriptions systems and general pratice) ­suplement only!
specialised registers ­(disease registers or special surveys) ­ better quality!
Population Data
population registers
census data
vital registration data
administration data
special surveys
•Problems (Lawson, A.B., 2001):
•­diagnostic «fashion» changes over time
•­code differences in space and time
•­boundary changes (MAUP ­ modifiable area unit problem)
•To be considered: edge effects and the scales of measurement (Lawson, A.B., 2001)
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Data Considered for this Study:
Requirements (Cliff, A.D. ET AL, 1981):
Replicability
Stability over space and time
Observability
Isolation
Simplicity of transmission process
High level of data accuracy
Others
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Data Considered for this Study:
Possible Sources:
Monthly numbers of reported cases of measles for each of the medical districts of Iceland (2
waves: 1896-1975, 1945-1970) and monthly estimates of the numbers of individuals at risk
(S population*). SI model. (Cliff, A.D. ET AL, 1981).
Centers for Disease Control and Prevention
• http://www.cdc.gov/scientific.com
- Surveillance: 121 cities mortality report: year, week, location (USA cities) (Cliff, A.D. ET
AL, 1998)
- HIV/AIDS surveillance report (morbidity data weekly, by city)
- Surveillance Resources of infectious diseases - Lyme disease cases and population reported
by state (1990-1999).
- tuberculosis surveillance reports - tuberculosis cases and case rates, by year, by state.
•*Cohort
Model
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Cellular automata
«Contrary from intuition, complexity can arise from simple rules» (Wolfram, S, 2002)
Traditional approach to systems study: assume that rules to explain the systems are based on traditional
mathematics.
Breaking the systems down to find their underlying parts can give us an a idea of how the components
act together to produce some of the most obvious features of the overall behaviour!
Top Down - The relationships of interest are between variables that capture the global properties of a
natural system.
Bottom up - Start from a description of local interactions. Analysis and computer simulation
should produce, as emergent properties, the global relationships seen in the real world, without
these being pre-programmed into the model!!
•An agent-based model is a bottom up model defined in terms of an algorithmic
•description of the behaviour and interactions of individuals (Sumpter, D.J.T)
Artificial life, discrete event
simulations, cellular automata,...
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Cellular Automata (cont.)
Discrete dynamical systems whose behaviour is
completely specified in terms of a local relation
(Toffoli ET AL, 1991)
System laws are local and uniform
- Neighbourhoods: More, von Neumann, Margolus
- Rules: deterministic, probabilistic, voting
CA classes I, II, III, IV (in class IV moving structures are present that allow the comunnication of information))
With appropriate IC, class IV can mimic the behave of all sorts of systems ! (Wolfram, S., 2002)
Recent Progress of ca:
Technological side: computers that can carry the
directives of a CA model in a efficient way
conceptual side: we are learning how to construct
discrete distributed models wich capture essential
aspects of physical casuality
Virtues of CA:
Inherently parallel: if we associate a processor with every N cells, we can multiply the size of the simulation
indefinitly without increasing the time taken for each complete updating of the space.
Inherently local: locality of interconnection of simple processing elements can be translated into speed of
operation (speed light constraint).
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Epidemiology and CA
The biology of the host-pathogen interactions is so complex that there is a tendency to allow models
to become increasingly complex, making them computationally intensive, with many parameters,
and difficult to analyse.
Good approach: simpler models which, nevertheless, have the ability to reproduce the behaviour of real
systems.
Aplications
Plant epidemiology (Newton, A.C. ET AL) - in contrast to
animal populations, plant populations are unable to mix freely,
and whether an individual plant is healthy or diseased is often
closely related to the state of other plants in its immediate
neighbourhood.
Wildlife diseases (Thulke H ET AL) - the host population is not
homogeneously affected by the disease over time (the regional
spatial pattern emerges from the particular disease dependent
dynamics, on the level of the respective local units of infection).
The disease dynamics within one local unit of infection is simply a
finite number of finite states wich follow up according to time
dependent transition probabilities and external stochastic.
Model for the spread of an aerially disseminated foliar disease in a
mixed cultivar crop(A.C. Newton, G. Gibson & D. Cox)
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Epidemiology and CA (cont.)
Lattice gas cellular automaton (LGCA) for a generic SIR
(Fuk´s, H. ET AL) - Unlike models based on partial diferential
equations the spread of the infection occurs due to the motion
of individuals and their interactions.
The model allows to investigate effects of spatial
inhomogeneities in population, concentrations on the dynamics
of epidemic processes and vaccination strategies.
Advantages of CA epidemic models:
LGCA dynamics evolution under a uniform vaccination
strategy (Fulk's, H. ET AL)
LGCA dynamics evolution under a barrier vaccination
strategy (Fulk's, H. ET AL)
- treat individuals in biological populations as discrete
entities
- allow to introduce local stochasticity
- well suited for computer simulations
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
(My) CA model
•Formulate real model
•Validate model
•
•Assumptions •for model
•Formulate CA model
•Interpret •Run CA model
solution
•
•Use model to explain, predict, decide, design
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Building a CA model: what is available?
Software Packages/Programming Languages for CA
SWARM - KENGE
MAML
STARLOGO
CASE
CELLANG
...
Programming Libraries for CA development
Integrating modelling toolkit
BIOME
SIMEX
Xtoys
...
General Software Packages for Mathematical Models General GIS packages
Matlab - mapping toolbox
Scilab
Mathematica
...
GRASS - MAGICAL
ArcGis
IDRISI
...
COM objects for GIS development
MapObjects
ArcObjects
...
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Solutions????
Programming a model and linking it to a GIS using I/O files
http://www.cobblestoneconcepts.com/ucgis2summer/liang/liang.htm
http://www.gisdevelopment.net/aars/acrs/2000/ts12/ts12003.shtml
Developing the model inside the GIS using a scripting language
Developing the model outside the GIS using COM components (MapObjects,
ArcObjects,...)
http://www.casa.ucl.ac.uk/joanasimoes/
Are GIS capacities that relevant in this context????
Using CA software packages, mathematical packages or building an aplication from scratch
•Aplication
using ESRI MapObjects
http://www.casa.ucl.ac.uk/joanasimoes/
•
Aplication using KENGE libraries
http://www.gis.usu.edu/swarm/
•
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
for
SWARM
Geographic Resources Analysis Support System
http://grass.itc.it
GRASS is an open-source GIS distributed under the GNU license.
It supports common vector and raster aplications, with enphasis on raster
aplications.
Provides environmental modelling such as CA for wildfire simulation.
Programming within GRASS: the open arquitecture of GRASS allows new
functions to be implemented as native code rather than as scripts linking existing
programs: this is essential to computationally intensive methods as simulation
(Lake, M. W., 200)
There is a multiagent simulation extension for GRASS, created by Lake, M. W.,
(2000):
MAGICAL - http://www.ucl.ac.uk/~tcrnmar/
•A
Random Walk genotype generated by MAGICAL (genotypes determine agent activities)
http://www.ucl.ac.uk/~tcrnmar/simulation/magical/examples/node1.html
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
Contacts
Mail: [email protected]
Main url: http://www.joana.fr.fm
Msc url: http://www.casa.ucl.ac.uk/joanasimoes
This presentation is available on:
http://casoco.casa.ucl.ac.uk/joana/phd/phd.htm
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
References:
Adami, Christoph. (1998) «Introduction to artificial life» - Springer/TELOS, New York. xviii, 374p.
Chopard, B.; Droz,M.; (1998) «Cellular Automata Modelling of Physical Systems» section Aléa Saclay; Cambridge
University Press, UK. 341p.
Wolfram, S.; (2002) «ANew Kind of Science», Wolfram Media INC
Toffoli; Margolus; (1991) «Cellular Automata Machines» MIT Press Series in scientific computation, USA. 259p.
Cox, D. R. ; Anderson, R. M.; Hillier, Hilary C.; (1989) «Epidemiological and statistical aspects of the AIDS
epidemic»- Royal Society, London. 149p.
Cliff, A.D, Hagget, P.; Smallman-Raynor, M. (1998) - «Deciphering Global Epidemics - Analytical approaches to the
disease records of world cities, 1888-1912”. Cambridge Studies in Historical Geography. Cambridge University
Press. 470 p.
Cliff, A.D.; Hagget, P.; Ord, J.K.; Versey, G.R.; (1981) «Spatial Diffusion - An historical geography of epidemics in
an island community» Cambridge University Press, Cambridge. 238p.
Diekmann, O.; Heesterbeek, J.A.P. (2000) «Mathematical Epidemiology of Infectious Diseases» model building,
analysis and interpretation - Wiley series in Mathematical and Computational Biology; John Wiley & Sons, NY.
303p.
Lawson, Andrew. B.; (2001) «Statistical Methods in Spatial Epidemiology» Wiley series in probability and statistics.
John Wiley & Sons, England.
P. Elliot, John Wakefield, Nicola Best, David Briggs (2000) «Spatial Epidemiology - Methods and Applications» ,
Oxforf University Press
Banks, Robert B. (1994) - «Growth and diffusion phenomena » mathematical frameworks and applications Springer Verlag, USA. 428 p.
Gladwell, M.; (2000) «The Tipping Point - How litle things can make a big difference» Litle Brown and Company,
USA. 279p.
Cliff, A.D.; Gould, P.R.; Hoare, A.G.; Thrift, N. J.; (1995) «Diffusing Geography» Blackwell Publishers Inc. 414p.
Dauphiné, A.; (1995) «Chaos, Fractales et dynamiques en géographie» Glip RECLUS, Montepellier. 136p.
Burghes, D.N.; Borrie, M.S.; (1981) - «Modelling with differential equations» - John Wiley & Sons. 172 p.
Lake, M. W.; (2000) - «MAGICAL computer simulation of Mesolithic foraging». In Kohler, T. A. and Gumerman, G.
J., editors, Dynamics in Human and Primate Societies: Agent-Based Modelling of Social and Spatial Processes,
pages 107-143. Oxford University Press, New York.
A.C. Newton, G. Gibson & D. Cox - «Understanding plant disease epidemics through mathematical modelling»
Azra C. Ghani*, Neil M. Ferguson, Christl A. Donnelly, Thomas J. Hagenaars and Roy M. Anderson (1998) «Epidemiological determinants of the pattern and magnitude of the vCJD epidemic in UK »
David J.T. Sumpter. « Models»
•
Thulke H H, Grimm V, Jeltsch F, Tischendorf L, M_uller T, Selhorst T, Staubach C, Wissel C«Cellular automata
in epidemiology - a modelling concept and a wildlife disease»
Henryk Fuk´, Anna T. Lawniczak - «Individual-based lattice model for spatial spread of epidemics»
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses
References (cont.):
http://www.maml.hu/
http://www.swarm.org/
http://sourceforge.net/projects/imt/
http://education.mit.edu/starlogo/starterpage.html
http://wosx30.eco-station.uni-wuerzburg.de/~martin/biome/
http://www.iu.hio.no/~cell/
http://www.la.utexas.edu/lab/software/lib/simex/README.html
http://www.vbi.vt.edu/~dana/ca/cellular.shtml
http://www.physics.mun.ca/~johnw/xtoys.html
http://www.matlab.com
http://www-rocq.inria.fr/scilab/
http://www.cobblestoneconcepts.com/ucgis2summer/liang/liang.htm
http://www.stephenwolfram.com
http://grass.itc.it
http://www.geog.ucsb.edu/~kclarke/ucime/banff2000/78-mu-paper.htm
http://www.gisdevelopment.net/aars/acrs/2000/ts12/ts12003.shtml
http://www.gis.usu.edu/swarm/
Using GIS a nd CA to stud y the Prop a g a tion of Infec tious Disea ses