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Epidemic Models with Varying Infectivity on a Refining Spatial Grid—I—The SI Model

Author

Listed:
  • Anicet Mougabe-Peurkor

    (Laboratoire de Mathématiques et Applications, Université Félix Houphouët-Boigny, Abidjan BP V34, Côte d’Ivoire)

  • Étienne Pardoux

    (CNRS, Aix Marseille Université, I2M, 13003 Marseille, France)

  • Ténan Yeo

    (Laboratoire de Mathématiques et Applications, Université Félix Houphouët-Boigny, Abidjan BP V34, Côte d’Ivoire)

Abstract

We consider a space–time SI epidemic model with infection age dependent infectivity and non-local infections constructed on a grid of the torus T d = [ 0 , 1 ) d , where the individuals may migrate from node to node. The migration processes in either of the two states are assumed to be Markovian. We establish a functional law of large numbers by letting the initial approximate number of individuals on each node, N , to go to infinity and the mesh size of the grid, ε , to go to zero jointly. The limit is a system of parabolic PDE/integral equations. The constraint on the speed of convergence of the parameters N and ε is that N ε d → ∞ as ( N , ε ) → ( + ∞ , 0 ) .

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2826-:d:1476468
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    References listed on IDEAS

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    1. Andersson, Håkan & Djehiche, Boualem, 1995. "Limit theorems for multitype epidemics," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 57-75, March.
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