Journal of Mathematical Biology

, Volume 28, Issue 4, pp 365-382

First online:

On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations

  • O. DiekmannAffiliated withCentre for Mathematics and Computer ScienceInstitute of Theoretical Biology, Leiden University
  • , J. A. P. HeesterbeekAffiliated withCentre for Mathematics and Computer Science
  • , J. A. J. MetzAffiliated withInstitute of Theoretical Biology, Leiden UniversityCentre for Mathematics and Computer Science

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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