Math 449
Dynamical systems in Biology
and Medicine.
D. Gurarie
Overview
Living world
Structure/Organization
Function/Process
Pathogens/Diseases
Genom
Cell
Epithelial
Connective
Muscular
nervous
Skeletal
Digestive
Respiratory
Endocrinal
Immune …
Expression
Reproduction
Regulation
Tissue
System
Organism
Population
Eco system
Environment
Signaling:
chemical (enzyme kinetics)
neural
Anatomy, physiology, behavior
(e.g. locomotion
adaptation, migration, invasion)
Species interaction:
competition/cooperation
(symbiosis, parasitism)
Dynamic Modeling
• Model Structure:
– State space (variables and parameters)
– Model type: discrete, continuous, deterministic, stochastic,…
– Mathematical tools/techniques: differential equations, discrete
eq-ns, combinatorial structures (graphs, networks, etc.)
– Computer tools
Objectives, strategies:
•Build “mathematical cartoons” of real (physical, chemical, biological)
systems
•analyze, identify dynamic patterns (e.g. equilibria, cycles, chaos).
•Develop math. concepts, tools and techniques (analytic, numeric,
exact, qualitative)
•Solution methods for predicting outcomes
•Parameter estimation and model validate
Applications:
•explain data
•make predictions
•test hypotheses
•run numeric (virtual) experiments, compare with real/
data/experiments