Math 6102
Mathematical Biology

Winter, 2012

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: Limiting systems and chain transitive sets
• Interacting Populations Models
  • Predator-prey models
  • Competition models
  • Mutualism models
  • Appendix: 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
  • Appendix: Basic reproduction numbers for compartmental models
• Biological Waves and Invasion Speeds
  • Fisher waves and bistable waves
  • A spruce budworm model with diffusion
  • The periodic Ross-Macdonald malaria model
  • Appendix: Spatial dynamics for monotone semiflows

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", Springer-Verlag, 2003.

Assignments:

• Assignment 1, Due date: January 26
• Assignment 2, Due date: February 14
• Assignment 3, Due date: March 13

Project Topics (for final exam):

Presentation Schedule: 2:00pm-5:00pm, HH-3017, April 9, 2012.