Kursernas Hemsidor

Simple dynamical systems and epidemical modelling

This web page contains parts of the material used in the course 273028 Special Course in Dynamical Systems (5 sp), given at the Department of Mathematics during period 2, 2009.

Course notes week 45
Lectures notes from weeks 44-45.
Examples of how to use wxMaxima and Octave.

General about math of epidemics
Good review math in known general epidemical models

Material on malaria

Introduction to disease Malaria
Introduction to Malaria Control modelling
A very nice review of most important results from simple math models by Koella
About vector-borne disease modelling from May and Andersson
Paper showing how to estimate model parameters by Nedelman
A linear model for age-dependence prevalency by Aron
A more complicated model which can be used for computer experiments for comparison with simpler by Chitnis

Codes for laborations Many codes are in Matlab which in recent time is getting more and more expensive and not available for most students. The same code file should however work for the free program Octave. Here we introduce some programs You can use for laborations:
To plot a two parameter linear phase portrait You can use the following matlab programs:
First use the parameter program to define the parameters of the four constants in the matrix giving the system (these are a,b,c,d if the system is x'=ax+by, y'=cx+dy). Then the plot program plots the phase portrait using the function file fun00a.m. As another example, some curves in figure 1 in my paper are created by this program using the function file above.
You can easily change the function in the function file to plot the phase portrait for other two dimensional systems.
Please also try for evaluation the new program using this arrow program where You click only once on the curve for getting the arrow.

Garki project

Senast uppdaterad: 5.11.2009