Persistence and Dynamics in Lattice Models of Epidemic Spread

We present a simple epidemic model representing the spread of a communicable disease in a spatially extended host population. The model falls into the general class of techniques which utilise lattice based simulation as a way of incorporating spatial effects. The factors relating to the persistence and dynamics of the disease are investigated. There exists a clear population threshold below which the disease dies out and above which it settles to an endemically stable state. The rate of population mixing is shown to affect this threshold density. Equations which accurately account for the mean-field limit of the model are introduced and the relevance to the epidemiological modelling of measles is discussed.