Models of epidemics and endemicity in genetically variable host populations

A discrete time genetics model is developed for populations that are undergoing selection due to infectious disease. It is assumed that the generation time of the host and infectious agent are not-synchronous and that only the host population is evolving. Two classes of epidemic processes are considered. The first class is for infectious agents that confer immunity following infection, while the second class is for those that do not confer immunity. The necessary and sufficient conditions are found in order for the disease to persist in a stable polymorphic host population. These conditions are shown to depend on the density of susceptibles, the selection coefficients, and the severity and class of the disease process.