Affiliation:
1. Laboratoire de Mathématiques et Applications, Université Félix Houphouët-Boigny, Abidjan BP V34, Côte d’Ivoire
2. CNRS, Aix Marseille Université, I2M, 13003 Marseille, France
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 Td=[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 Nεd→∞ as (N,ε)→(+∞,0).
Funder
MOPRODEP project
CNRS International Research Network AfriMath
Institut de Mathématiques de Marseille
University Félix Houphouët Boigny
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