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

Anicet Mougabe-Peurkor, Étienne Pardoux () and Ténan Yeo
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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

Mathematics, 2024, vol. 12, issue 18, 1-22

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 ) .

Keywords: epidemic model; varying infectivity; non-local infections; law of large numbers; integral equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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