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.
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Centre for Mathematics and Computer Science, P.O. Box 4079, 1009, AB Amsterdam, The Netherlands
O. Diekmann, J. A. P. Heesterbeek & J. A. J. Metz
Institute of Theoretical Biology, Leiden University, Kaiserstraat 63, 2311, GP Leiden, The Netherlands
O. Diekmann & J. A. J. Metz
Diekmann, O., Heesterbeek, J.A.P. & Metz, J.A.J. On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–382 (1990). https://doi.org/10.1007/BF00178324
Received: 30 May 1989
Revised: 07 November 1989
Issue Date: June 1990
DOI: https://doi.org/10.1007/BF00178324
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