Journal of Mathematical Biology

, Volume 28, Issue 4, pp 365–382 | Cite as

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

  • O. Diekmann
  • J. A. P. Heesterbeek
  • J. A. J. Metz


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 models Heterogeneous populations Basic reproductive number Invasion 


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • O. Diekmann
    • 1
    • 2
  • J. A. P. Heesterbeek
    • 1
  • J. A. J. Metz
    • 2
    • 1
  1. 1.Centre for Mathematics and Computer ScienceAB AmsterdamThe Netherlands
  2. 2.Institute of Theoretical BiologyLeiden UniversityGP LeidenThe Netherlands

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