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The asymptotic final size distribution of reducible multitype Reed-Frost processes

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The asymptotic final size distribution of a multitype Reed-Frost process, a chain-binomial model for the spread of infection in a finite, closed multitype population, is derived in the case of reducible contact pattern between types. The results are obtained using techniques developed for the irreducible case.

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  1. Bailey, N. T. J.: The mathematical theory of infectious diseases and its applications. Griffin, London 1975

  2. Ball, F.: The threshold behaviour of epidemic models. J. Appl. Probab. 20, 227–241 (1983)

  3. Gart, J. J.: The statistical analysis of chain-binomial epidemic models with several kinds of susceptibles. Biometrics 28, 921–930 (1972)

  4. Radcliffe, J., Rass, L.: The spatial spread and final size of the deterministic non-reducible n-type epidemic. J. Math. Biol. 19, 309–327 (1984)

  5. Scalia-Tomba, G.: Extensions of the Reed-Frost process. Thesis. University of Stockholm, Sweden (1983)

  6. Scalia-Tomba, G.: Asymptotic final size distribution of the multitype Reed-Frost process. J. Appl. Probab., in press (1985)

  7. Seneta, E.: Non-negative matrices and Markov chains. Springer, Berlin, Heidelberg, New York (1981)

  8. Sewastjanow, B. A.: Verzweigungsprozesse. Akademie Verlag, Berlin (1974)

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Scalia-Tomba, G. The asymptotic final size distribution of reducible multitype Reed-Frost processes. J. Math. Biology 23, 381–392 (1986). https://doi.org/10.1007/BF00275255

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Key words

  • Chain-binomial process
  • Final epidemic size
  • Asymptotic distribution
  • Multitype epidemic model
  • Reducible contact structure