COURSE OUTLINE COURSE OUTLINE
Math 6780
Mathematical Biology II
Spring Semester, 2007

The details of the outline and the readings are likely to change based on student interest, but the overall plan will probably not. I will either post the readings on the web page, hand them out, or tell you not to bother.

Week Topic Reading
Epidemiological dynamics
January 9 R0 and the next generation operator [1]
January 16 Connectivity [2,3]
January 23 Spatial epidemics [4]
January 30 Interacting diseases [5]
February 6 Macroparasites [6]
February 13 Stochastic epidemics [7]
February 20 Seasonality and oscillations [8,9,10]
Fitting models to data
February 27 Maximum likelihood and the AIC [11]
March 6 Bootstrapping and generalized cross-validation [12]
March 13 Markov Chain Monte Carlo [13]
Evolution and genetics
March 27 Evolution of virulence [14,15,16]
April 3 Group selection models [17]
April 10 Quasispecies models [18,19]
April 17 Evolution of genetic robustness [20,21]
April 24 Project presentations

References

[1]
Diekmann, O., Heesterbeek, J. A. P., and Metz, J. A. J. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology 28, 365-382 (1990).

[2]
Adler, F. R. and Nuernberger, B. Persistence in patchy, irregular landscapes. Theoretical Population Biology 45, 41-75 (1994).

[3]
Diekmann, O., Jong, M. C. M. D., and Metz, J. A. J. A deterministic epidemic model taking account of repeated contacts between the same individuals. Journal of Applied Probability 35, 448-462 (1998).

[4]
Medlock, J. and Kot, M. Spreading disease: Integro-differential equations old and new. Mathematical Biosciences 184, 201-222 (2003).

[5]
Adler, F. R. and Mosquera, J. Is space necessary? Interference competition and limits to biodiversity. Ecology 81, 3226-3232 (2000).

[6]
Adler, F. R. and Kretzschmar, M. Aggregation and stability in parasite-host models. Parasitology 104, 199-205 (1992).

[7]
McNeil, D. On the simple stochastic epidemic. Biometrika 59, 494-497 (1972).

[8]
Rohani, P., Green, C., Mantilla-Beniers, N., and Grenfell, B. Ecological interference among fatal infections. Nature 422, 885-888 (2003).

[9]
Adler, F. R., Pearce-Duvet, J. M. C., and Dearing, M. D. How host population dynamics translate into time-lagged prevalence: An investigation of sin nombre virus in deer mice. Bulletin of Mathematical Biology , (to be submitted) (2007).

[10]
Dushoff, J., Plotkin, J. B., Levin, S. A., and Earn, D. J. D. Dynamical resonance can account for seasonality of influenza epidemics. Proc. Nat. Acad. Sci. 101, 16915-16916 (2004).

[11]
Edwards, A. W. F. Likelihood. Cambridge University Press, Cambridge, (1972).

[12]
Ellner, S. P. and Guckenheimer, J. Dynamics models in biology. Princeton, (2006).

[13]
Clark, J. S. Models for Ecological Data: An Introduction. Princeton, (2007).

[14]
Mosquera, J. and Adler, F. R. Evolution of virulence: A unified framework for coinfection and superinfection. Journal of Theoretical Biology 195, 293-313 (1998).

[15]
Claessen, D. and de Roos, A. M. Evolution of virulence in a host-pathogen system with local pathogen transmission. Oikos 74, 401-413 (1995).

[16]
Gandon, S., Mackinnon, M. J., Nee, S., and Read, A. F. Imperfect vaccines and the evolution of pathogen virulence. Nature 414, 751-756 (2001).

[17]
Wilson, D. S. The natural selection of populations and communities. Benjamin/Cummings Pub. Co., Menlo Park, Calif. QH 375.W54, (1979).

[18]
Wilke, C. O. Quasispecies theory in the context of population genetics. Bmc Evolutionary Biology 5, 44 (2005).

[19]
Bull, J. J., Meyers, L. A., and Lachmann, M. Quasispecies made simple. Plos Computational Biology 1, 450-460 (2005).

[20]
Krakauer, D. C. and Plotkin, J. B. Redundancy, antiredundancy, and the robustness of genomes. Proc. Nat. Acad. Sci. 99, 1405-1409 (2002).

[21]
Wilke, C. O. and Adami, C. Evolution of mutational robustness. Mutation Research 552, 3-11 (2003).


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On 18 Jan 2007, 12:04.