Matrix models for stage-classified epidemics

The demographic time-scale is usually very different from the epidemic time-scale, so most models focus either on demographic or epidemic questions.  But, most infectious diseases affect different stages of the host population in a different way.  In order to know how recurring epidemics, or epidemics that have long infectious period, such as HIV/AIDS, affect the population, the model should incorporate both realistic demographic and epidemic detail.  To allow for demographic detail in each epidemic compartment, we have constructed a matrix model by generalizing the vec-permutation matrix approach to spatial models, developed by Hunter and Caswell, to a model that classifies individuals by demographic stage and epidemiological status. We find that the combined matrix model changes the dynamics of its building blocks; a simple demographic model and the basic SIR model.