Math 449 Dynamical systems in Biology and Medicine.
-
Upload
mason-kent -
Category
Documents
-
view
20 -
download
4
description
Transcript of Math 449 Dynamical systems in Biology and Medicine.
Math 449Dynamical systems in Biology
and Medicine.D. Gurarie
Overview
Structure/Organization
Genom
Cell
Tissue
System
Organism
Population
Eco system
Environment
Function/Process
Signaling:chemical (enzyme kinetics)neural
Expression ReproductionRegulation
Species interaction:competition/cooperation(symbiosis, parasitism)
Anatomy, physiology, behavior(e.g. locomotionadaptation, migration, invasion)
EpithelialConnectiveMuscularnervous
SkeletalDigestiveRespiratoryEndocrinal
Immune …
Pathogens/Diseases
Living world
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