Math 6102 Mathematical biology
This course is an introduction to mathematical biology. The contents include Single Species Models (the Verhulst model, a spruce budworm model, microorganism growth in a chemostat, and an appendix on limiting systems and chain transitive sets); Interacting Populations Models (predator-prey models, competition models, mutualism models, and an appendix on uniform persistence in dissipative systems); Dynamics of Infectious Diseases (the Kermack-McKendrick model, a multi-type SIS epidemic model, an epidemic model in a patchy environment, and an appendix on basic reproduction numbers
for compartmental models); and Biological Waves and Invasion Speeds.
Ordinary differential equations and dynamical systems at the undergraduate level.
- J. D. Murray, Mathematical Biology, I: An introduction, Springer-Verlag, 2002.
- H. R. Thieme, Mathematics in Population Biology,
Princeton University Press, 2003.
- X.-Q. Zhao, Dynamical Systems in Population Biology, second edition,