GCI2016: Mini-course 3: Basic Mathematical Models... - Lecture 2: Jacek Banasiak

Mini-course 3: Basic Mathematical Models in Epidemiology and Species
Invasion
Jacek Banasiak, University of Pretoria
General description: The workshop brings together participants with different
backgrounds and levels of exposure to mathematical modelling. This mini-course aims at
introducing notions that occur in modelling processes in life science such as discrete and continuous dynamical systems, modelling interactions, stability and long term behaviour of
evolutionary processes. These concepts will be illustrated on compartmental models of
mathematical epidemiology. We shall also discuss species and disease invasion modelled by
reaction diffusion equations and their travelling wave solutions.
Lecture 1: Principles of mathematical modelling
a. Discrete versus continuous time, autonomous versus non-autonomous, linear
versus nonlinear
b. Modelling intra and inter-species interactions: mass action, Holling, etc
c. Basic single species models in discrete and continuous time
d. Concepts of stability in dynamical systems
Lecture 2: Common epidemiological models
a. Principles of construction of compartmental models: SI, SIR, SIS etc
b. Vector-borne diseases: malaria model
c. Basic questions and methods of analysis
d. Some pitfalls in modelling
Lecture 3: Invasion modelling
a. Population models with space structure
b. Travelling waves
c. Examples.