Mathematical models in the biological sciences, systems,
phase-plane analysis, diffusion, convective transport,
bifurcation analysis. Possible applications will include
population models, infectious disease and epidemic models,
acquired immunity and drug distribution, tumor growth, and
analysis of arterial flow dynamics.
Additional Requirements for Graduate Students: Extra problems on weekly homework or a term project.
Athena Title
Mathematical Biology
Prerequisite
(MATH 2270 or MATH 2270H or MATH 2500 or MATH 2500E or MATH 3510 or MATH 3510H) and (MATH 4700/6700 or MATH 2700 or MATH 2700E)
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Student Learning Outcomes
Students will understand how to model biological phenomena using systems of differential equations as well as probability theory.
Students will understand how to analyze the qualitative behavior of mathematical models in order to uncover such features as diffusion and bifurcations.
Students will understand how to compare the results of mathematically analyzing models of biological phenomena to experimental and clinical data.
Topical Outline
Discrete-time and continuous-time population models; prey-predator models; interacting species models.
Phase plane analysis and stability in two-dimensional ODE models; bifurcation analysis.
A selection of additional application topics, which may vary between course offerings, chosen from among: reaction kinetics; enzymatic reactions and gene regulation; biological oscillators; stochastic modelling; dynamics of epidemics; reaction-diffusion systems; biological waves; dynamics of the vascular network; growth and control of tumors; and systems biology.
