Endemic Disease in Environments with Spatially Heterogeneous Host Populations*

The main interest in epidemic models stems from their use in uncovering certain qualitative features of epidemic processes. A deterministic model of a general epidemic in a population with an arbitrary number of separate population centers is presented. The mixing within each center is assumed to be homogeneous, and the usual threshold theorem holds for each population. The mixing between centers is nonhomogeneous. This model is used to identify the necessary and sufficient conditions under which a disease will become endemic in the general population when each population center is below the threshold required for establishment of the disease and does not mix with other centers. These conditions depend critically on the concavity of the infection rate function with respect to the length of exposure time. The application of these results to host-vector models is discussed.