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Convergence of a finite volume scheme for nonlocal reaction-diffusion systems modelling an epidemic disease

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  • A finite-volume scheme for a nonlocal three-component reaction-diffusion system modeling an epidemic disease with susceptible, infected, and recovered, individuals is analyzed. For this SIR model, the existence of solutions to the finite volume scheme and its convergence to a weak solution of the PDE is established. The convergence proof is based on deriving a series of apriori estimates and by using a general $L^p$ compactness criterion. Finally, numerical simulations from the finite volume scheme are given.
    Mathematics Subject Classification: 35K57, 92C15, 92C60, 65M12.

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