Models for the Study of Infection in Populations

John R. Williams

This chapter provides an overview of the modeling of transmission dynamics of infectious diseases, with particular focus on the use of compartmental differential equation models, the most commonly used for such work. An introduction including a brief description of historical antecedents is followed by a section putting such modeling in its ecological context. The next section discusses some of the characteristics of infection in populations that are determinants of the observed population dynamics of infection. This is followed by a brief section considering the scope and limitations of dynamic models, followed by a section summarizing some of the key concepts relevant to this type of modeling work. Simple ordinary differential equation models are introduced in the next section. Demography and the relevance of population age structure to infection transmission dynamics, and partial differential equation models incorporating age structure and age-related processes of infection and disease, are explored in the following two sections. The section after this considers three examples of infections in which age-related processes are important. Next there is a brief look at alternative approaches to modeling, and the penultimate section introduces further uses for dynamic models in health economic analysis, immune system dynamics, and exploring the impact of strain variation in infections. The concluding section is followed by a short appendix on the solution of differential equation system models.

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