Chapter 7 - Spatial Models

It is intuitive that in most circumstances, disease transmission is predominantly a localized process. For directly transmitted diseases, for example, transmission is most likely between individuals with the most intense interaction, which generally implies those in the same location. Additionally, movement of individuals between population centers facilitates the geographical spread of infectious diseases. This chapter is concerned with capturing these host population characteristics, enabling us to address issues such as: determining the rate of spatial spread of a pathogen, calculating the influence of large populations on smaller ones, and finding optimally targeted control measures that take into account the local nature of spatial transmission. Generally, models of this sort operate by partitioning the population according to the spatial position of hosts, such that nearby hosts are grouped together and interact more strongly. A wide variety of model formats have been developed to accomplish this, with the primary differences being the scale at which hosts are aggregated; although no definitive rules exist. Rigorous analytical results for spatial epidemiological models remain rare. Since the late 1980s, however, the increasing ease of access to computational power has permitted the detailed simulation of such models. Frequently, these models incorporate stochasticity, so readers may wish to familiarize themselves with Chapter 6 before continuing.