Instructor: Yang Kuang; Office: PSA 429; PHONE (480) 965-6915, kuang@asu.edu

SYLLABUS -APM 534-Fall, 2011, Kuang

APM 534-Mathematical Population Biology, II

86580, T Th 3:00 PM - 4:15 PM, 8/18/11  - 12/6/11, Tempe PSA 307

Office hours: W: 1pm-3pm, Th. 1pm-2pm.

Mathematical Population Biology II selectively covers population biology models in the form of partial differential equations and systems. The course will focus on mathematical analysis of population models as well as model formulation and simulation. Specifically, it will cover most of the following topics.

1): Derivation of one dimensional conservation equations. The flux terms give rise to transport equations and diffusion equations. Computation of average times taken in diffusion models to diffuse a given distance and, in models with chronological or class age structure, survival/sojourn probabilities and sojourn/life expectations.

2): Population dispersal models based on reaction-diffusion equations. Random and chemotactic motion of microorganisms. Directed diffusion. Spatially uniform and non-uniform steady states. Finite time blow-up.

3): Existence and properties of traveling waves in models of genetic dispersion, colonies of microorganisms, species invasion and infectious diseases. Spreading speed: for example, traveling waves and spreading speeds in Fisher's equation, predator-prey models, and the spatial Kermack/McKendrick/Kendall model.

4): Models for development and pattern formation in biological and ecological systems.  Cellular slime molds model. Stability of homogeneous steady states, conditions for diffusive instability. Effects of habitat size and structure on species survival.

5): Epidemic models with chronological or class age structure. Disease extinction and persistence, periodic solutions. Reproduction number, stability/instability of steady states.

Textbook: Mark Kot, Elements of Mathematical Ecology, Cambridge U. Press, 2001.

References: 

1). Mathematical Biology I and II, by J. D. Murray, Springer-Verlag, 2002.

2). Leah Edelstein-Keshet , Mathematical Models in Biology, by, SIAM , 2005.

Grades are based on: 4 assignments, each 100 points, plus a take home final exam of 100 points, or the first two assignments and a project. If you plan to use this course for the comprehensive exam, you shall take the final.

HW #1, due on Thursday, Sept. 8: