Math 6102
Mathematical Biology

Winter, 2026

Text:

J. D. Murray, "Mathematical Biology, I: An introduction", Springer-Verlag, 2002.

Evaluation:

Course Contents:

• Single Species Models
  • The Verhulst (logistic) model
  • A spruce budworm model
  • Microorganism growth in a chemostat
  • Appendix: Chain transitive sets and limiting systems
• Interacting Populations Models
  • Predator-prey models
  • Competition models
  • Mutualism models
  • Appendix: Uniform persistence and coexistence states
• Dynamics of Infectious Diseases
  • The Kermack-McKendrick model
  • A multi-type SIS epidemic model
  • An epidemic model in a patchy environment
  • Appendix: Basic reproduction numbers for compartmental models
• Biological Waves and Invasion Speeds
  • Traveling waves and spreading speed
  • Bistable waves and stability
  • A spruce budworm model with diffusion
  • A nonlocal multi-type SIS epidemic model

Reference Books:

• D. S. Jones and B. D. Sleeman, "Differential Equations and Mathematical Biology", Chapman & Hall/CRC, 2003.
• H. L. Smith and P. Waltman, "The Theory of the Chemostat: Dynamics of microbial competition", Cambridge University Press, 1995.
• H. R. Thieme, "Mathematics in Population Biology", Princeton University Press, 2003.
• X.-Q. Zhao, "Dynamical Systems in Population Biology", second edition, Springer-Verlag, 2017.

Assignments:

Project Topics (for final exam): (to be annouced)

Presentation Schedule: (to be annouced)