Mathematical Ecology and Epidemiology

Overview

An introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.

Content

(i) Review of simple ODE models in ecology such as the logistic and Lotka-Volterra models. Extensions of such models such as the use of the Holling functional responses. Phase plane analysis of such models.

(ii) ODE models in epidemiology. The Kermack McKendrick model. Higher dimensional models that include, for example, an exposed compartment, or which incorporate treatment, vaccination or quarantining. Analytical techniques useful in the linearised analysis of high dimensional systems, such as the Routh Hurwitz conditions. The calculation of the basic reproduction number and its importance in epidemiological modelling.

(iii) Age structured models and their reformulation into delay differential equations or renewal integral equations. The study of the characteristic equations resulting from the linear stability analysis of such models. Use of such equations in ecology and epidemiology, to include the Ross Macdonald model of malaria transmission. The basic reproduction number for models with delay.

(iv) Reaction-diffusion equations. Travelling wave solutions; applications to ecology and epidemiology.  

Selected Texts

Background Reading

  • J.D. Murray: Mathematical Biology: I. An Introduction. Springer (2002).

  • N.F. Britton. Essential Mathematical Biology. Springer (2003).

Page Owner: mt0019
Page Created: Tuesday 27 November 2012 10:47:11 by mt0019
Last Modified: Tuesday 27 November 2012 14:40:46 by mt0019
Expiry Date: Thursday 27 February 2014 10:46:55
Assembly date: Wed Sep 17 19:27:14 BST 2014
Content ID: 94538
Revision: 1
Community: 1226