Population dynamics in spatially explicit lattice epidemic models

Presented is a computational implementation simulating the propagation of an infectious disease through a host population extended over a 2-dimensional square lattice. The model incorporates the effects of spatial distribution allowing for an analysis of the persistence and dynamics of the disease. Computational issues are discussed along with the results of the simulations. The simulations show that there is a threshold or critical population density. Below the critical density the disease dies out and above it, the disease persists endemically. Population mixing affects the disease's ability to persist and, hence, the critical density. Higher degrees of mixing improve a disease's ability to persist. The model is then studied analytically in the mean-field point approximation limit. Higher mean-field approximations, which better account for the spatial inhomogeneities of the spatially discrete computational model, are also considered.