Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation, and immunization programs

Abstract

Deterministic models are presented for epidemics which occur quickly and for long-term endemic diseases where births and deaths must be considered. Contact-rate matrices are formulated in terms of activity levels and subpopulation sizes by using a proportionate-mixing assumption. Methods are presented for estimating epidemic and endemic parameters in both homogeneous and heterogeneous populations. Other authors' approaches to contact-rate matrices and spatial heterogeneity are described. Three immunization programs are analyzed for a model of a spatially heterogeneous population and are compared in a “city and villages” example.