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The final size and severity of a generalised stochastic multitype epidemic model

  • Frank Ball (a1) and Damian Clancy (a1)

Abstract

We consider a stochastic model for the spread of an epidemic amongst a population split into m groups, in which infectives move among the groups and contact susceptibles at a rate which depends upon the infective's original group, its current group, and the group of the susceptible. The distributions of total size and total area under the trajectory of infectives for such epidemics are analysed. We derive exact results in terms of multivariate Gontcharoff polynomials by treating our model as a multitype collective Reed–Frost process and slightly adapting the results of Picard and Lefèvre (1990). We also derive asymptotic results, as each of the group sizes becomes large, by generalising the method of Scalia-Tomba (1985), (1990).

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* Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.

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Work carried out while Damian Clancy was in receipt of an SERC research studentship.

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References

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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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