Structured Populations with Nonlinear, Nonlocally Dependent Dynamics: Basic Theory

We review a method for modeling prevalence of disease in a population which is structured by the dependent variables from a density model for the disease. Our special interest is in models which exhibit nonlocal dependence, that is, where the dynamics of the course of disease depend on the global distribution of the population over its density structure. We give a short justification of the model, but observe that in the case of nonlocal dependence, our justification needs a priori existence of solutions to the model equations. The establishment of existence and uniqueness of solutions to these equations is our primary result.