Epidemics in heterogeneous populations: Aspects of optimal vaccination policies

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Three models for epidemics among mgroups with applications to human diseases, especially socially and geographically heterogeneous populations, are considered. It is shown that the initial growth of each is an increasing function of the Frobenius root of R0 the matrix of reproductive ratios. A new way of looking at optimal vaccination is presented by linking policies to the growth rate of a new epidemic. Aspects of how to minimize the initial growth rate are analysed. In particular, we see that, when R0 has positive eigenvalues, we can find an explicit solution for the final optimal policy, and that there exists an extension of this policy which always gives the least possible growth rate at all stages of vaccination. © 1989 Oxford University Press.

Original languageEnglish
Pages (from-to)137-159
Number of pages23
JournalMathematical Medicine and Biology
Issue number3
Publication statusPublished - 1989


  • City-villages model
  • Expected growth rate
  • Frobenius root
  • Heterogeneous
  • Matrix of reproductive ratios
  • Optimal vaccination policies
  • Positive definite


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