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Math 449 Dynamical systems in Biology and Medicine.

Math 449 Dynamical systems in Biology and Medicine. D. Gurarie Overview. Living world. Structure/Organization. Function/Process. Genom. Cell. Expression Reproduction Regulation. Tissue. Epithelial Connective Muscular nervous. Signaling: chemical (enzyme kinetics) neural. System.

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Math 449 Dynamical systems in Biology and Medicine.

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  1. Math 449Dynamical systems in Biologyand Medicine. D. Gurarie Overview

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

  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

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