21 - Epidemics

Summary

Aims of the project

You are given some data describing the development of epidemics which occurred in various communities and are provided with a basic model describing the dynamics of such a system. You are then invited to analyse the data as best you can to discover the underlying behaviour of the disease and the response of the community to it. The model is based on a set of coupled first order differential equations. You must obtain approximate analytic solutions and full numerical solutions using the routines provided.

Mathematical ideas used

You will need to: work with coupled first order differential equations (Chapter 7). make linear approximations; know how to integrate simple linear first order equations; understand the least squares fit idea (Chapter 5);

MATLAB techniques used

The numerical techniques for differential equations are those first introduced in Chapter 7. The multi-parameter least squares fit package is that first described in Chapter 20.

For convenience, here is a list of relevant M-files, both standard ones and special ones provided for this particular project. You may have to modify some of these in the course of your study. In each case typing help will give information on the purpose and usage.

fludat.m – data for school flu epidemic

plagdat.m – data for Bombay plague

colddat.m – data for island cold epidemic

sirepi.m – SIR epidemic model integrator

sirfn.m – derivative function for the above

mparft.m – multi-parameter least squares fit

mparst3.m – example set up for the above

resid3.m – residuals function for the above lagsum.m – cumulative sum