Journal of Mathematical Biology

, Volume 28, Issue 4, pp 365–382

On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations

Authors

  • O. Diekmann
    • Centre for Mathematics and Computer Science
    • Institute of Theoretical BiologyLeiden University
  • J. A. P. Heesterbeek
    • Centre for Mathematics and Computer Science
  • J. A. J. Metz
    • Institute of Theoretical BiologyLeiden University
    • Centre for Mathematics and Computer Science
Article

DOI: 10.1007/BF00178324

Cite this article as:
Diekmann, O., Heesterbeek, J.A.P. & Metz, J.A.J. J. Math. Biol. (1990) 28: 365. doi:10.1007/BF00178324

Abstract

The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.

Key words

Epidemic modelsHeterogeneous populationsBasic reproductive numberInvasion

Copyright information

© Springer-Verlag 1990