Models of Mathematical Biology

Timetable

lectures 1-7 Population Dynamics

lectures 8-9 Infectious Diseases

lectures 9-12 Population Genetics and Evolution

lectures 12-15 Pattern formulation

Module aim (aims)

The aim of the course is to discuss basic models of mathematical biology. This is an imprtant and active area of research today. We intend to cover its most important areas. This includes population dynamics, infectious diseases, population genetics and evolution and pattern formulation. The models which we discuss lead to fascinating mathematical problems still having important applications.

Pre-requisites in terms of knowledge, skills and social competences (where relevant)

A student should have basic knowledge in mathematical analysis including differential equations. However, we shall strive to make the course self-contained.

Syllabus

1. Population dynamics (single species, population dynamics of interacting species, game dynamics).

2. Infectious Diseases (SIR models, models of epidemy, AIDS).

3. Population Genetics and Evolution (discrete dynamical systems in population genetics, continuous selection dynamics, mutation and recombination).

4. Pattern Formulation (Turing instability, Turing Bifurcations, activator-inhibitor systems).

Reading list

1. J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge 1998.

2. J. D. Murray, Wprowadzenie do biomatematyki, Wydawnictwo Naukowe PWN 2002.

3. J. D. Murray, Mathematical biology: I. Introduction. Springer 2002.

4. R. Rudnicki, Modele i metody biologii matematycznej. Część I: Modele deterministyczne, Instytut Matematyczny Polskiej Akademii Nauk, Warszawa 2014.

5. Nicholas F. Britton, Essential Mathematical Biology, Springer-Verlag, London 2003.

6. Ronald W. Shonkwiler, James Herod, Mathematical Biology. An Introduction with Maple and Matlab, Springer, Dordrecht, Heidelberg, London, New York 2009