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Limit theorems for multitype epidemics

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  • Andersson, Håkan
  • Djehiche, Boualem

Abstract

By means of the law of large numbers and the central limit theorem, we compare the spatial epidemic model proposed by Kendall with a sequence of multitype epidemics, viewed as Hilbert space-valued stochastic processes. In the limit, the fluctuation process turns out to be an infinite-dimensional Ornstein-Uhlenbeck process.

Suggested Citation

  • Andersson, Håkan & Djehiche, Boualem, 1995. "Limit theorems for multitype epidemics," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 57-75, March.
    • Handle: RePEc:eee:spapps:v:56:y:1995:i:1:p:57-75
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    References listed on IDEAS

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    1. Blount, Douglas, 1993. "Limit theorems for a sequence of nonlinear reaction-diffusion systems," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 193-207, April.
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    Cited by:

    1. Alexander Aurell & René Carmona & Gökçe Dayanıklı & Mathieu Laurière, 2022. "Finite State Graphon Games with Applications to Epidemics," Dynamic Games and Applications, Springer, vol. 12(1), pages 49-81, March.
    2. Anicet Mougabe-Peurkor & Étienne Pardoux & Ténan Yeo, 2024. "Epidemic Models with Varying Infectivity on a Refining Spatial Grid—I—The SI Model," Mathematics, MDPI, vol. 12(18), pages 1-22, September.

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