Population Dynamics
2015




Population movements at the fish market Seal population at River Don, Aberdeenshire



Abstract

The course will display mathematical methods and techniques in Population Dynamics, focusing on epidemiology. One goal of the course is to illustrate both the mathematical methods used in population dynamics and the epistemological approach necessary to achieve realistic and usable models. Deterministic (time-discrete and time-continuous) and Stochastic approaches will be considered. The course rests on elementary notions of Linear Algebra, Dynamical Systems and Probability and Statistics. However, most of the necessary ideas will be freshened up along the course.

Course Material and Literature

A course in Mathematical Biology, G de Vries, T Hillen, M Lewis, J Müller and B Schönfisch. SIAM, 2006, Philadelphia. ISBN: 978-0-898716-12-8.
Mathematical Epidemiology, F Bauer, P v d Driessche and J Wu (eds), Lecture Notes in Mathematics, 1945 (Mathematical Biosciences Subseries). Springer 2008, Berlin. ISBN: 978-3-540-78910-9.
Lecture notes:
Ch1: Time-discrete deterministic dynamics, Modeling ideas, examples.
Ch2: Continuous-time deterministic dynamics. Review of dynamical systems theory, Examples, Epidemiological models. Epidemiological indicators.
Ch3: Stochastic models: Markov Jump processes, examples. Branching processes.
Ch4: Stochastic (continued): Kolmogorov Forward Equation (KFE).
Ch5: The deterministic limit. Connection between Stochastic and Deterministic approaches, Advantages and limitations.
Ch6: Practical problems with stochastic simulations. Approximations to the KFE.
Ch 7: Student's presentations.

Participation

The course is intended for Ph D students and advanced undergraduate students. It will have a mathematic profile, while being also suitable for students in the natural sciences.

Home assignements

The last meeting of the course will be devoted to the participant's own presentations.
This part of the course will be planned together with the participants and adjusted to the actual conditions.