1. Math 449 Dynamical systems in Biology and Medicine. D. Gurarie Overview

2. Structure/Organization Genom Cell Tissue System Organism Population Eco system Environment Function/Process Signaling: chemical (enzyme kinetics) neural Expression Reproduction Regulation Species interaction: competition/cooperation (symbiosis, parasitism) Anatomy, physiology, behavior (e.g. locomotion adaptation, migration, invasion) Epithelial Connective Muscular nervous Skeletal Digestive Respiratory Endocrinal Immune … Pathogens/Diseases Living world

3. 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

4. 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