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

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June 2009, 11(4): 823-853. doi: 10.3934/dcdsb.2009.11.823

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

Mostafa Bendahmane ^1, and Mauricio Sepúlveda ^2,

1.	Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción
2.	CI2MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Received March 2008 Revised January 2009 Published April 2009

Abstract
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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.

Keywords: reaction-diffusion system, nonlocal SIR model., weak solution, Finite volume scheme.

Mathematics Subject Classification: 35K57, 92C15, 92C60, 65M1.

Citation: Mostafa Bendahmane, Mauricio Sepúlveda. Convergence of a finite volume scheme for nonlocal reaction-diffusion systems modelling an epidemic disease. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 823-853. doi: 10.3934/dcdsb.2009.11.823

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