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Epidemic Models, Deterministic

  1. J. A. P. Heesterbeek1,
  2. M. G. Roberts2

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a07015

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Heesterbeek, J. A. P. and Roberts, M. G. 2005. Epidemic Models, Deterministic. Encyclopedia of Biostatistics. 3.

Author Information

  1. 1

    University of Utrecht, Utrecht, The Netherlands

  2. 2

    Wallaceville Animal Research Centre, Upper Hutt, New Zealand

Publication History

  1. Published Online: 15 JUL 2005

Abstract

In this article, we briefly review some of the approaches to deterministic modeling of epidemic phenomena. We have chosen to structure the approaches by specific biological examples that exemplify a certain approach and that were, in addition, historically important in shaping the development of the deterministic theory. These examples are measles, malaria, helminth infections, and HIV. For types of models, we briefly discuss ODE models and PDE age-structured models of compartmental SIR-type (both for microparasitic agents), ODE models for helminth parasites, formulated in terms of average parasite load, and the more general microparasite models in terms of integro-differential equations. In the latter, there is flexibility in defining the infectivity of individuals as a function of infection-age, which does not exist in the compartmental models. We also discuss the way to calculate the basic reproduction ratio R0 for each class of models.

Keywords:

  • epidemiology;
  • deterministic models;
  • basic reproduction ratio