The aim of this paper is to outline the numerical solution of a reaction-diffusion system describing the evolution of an epidemic in an isolated habitat. The model we consider is described by two weakly coupled semi-linear parabolic equations and we introduce a finite difference scheme for its numerical solution. We study the behaviour of the exact solution by means of the numerical scheme. We show the positivity, the decrease and the decay to extinction of the numerical solution. Finally we report the results of the numerical tests; in these simulations we observe that the asymptotic behaviour of the reaction-diffusion system is the same as that of the associated ODE system (Kermack-McKendrick model).

Stability and asymptotic behaviour for the numerical solution of a reaction-diffusion model for a deterministic diffusive epidemic

LOPEZ, Luciano
1983-01-01

Abstract

The aim of this paper is to outline the numerical solution of a reaction-diffusion system describing the evolution of an epidemic in an isolated habitat. The model we consider is described by two weakly coupled semi-linear parabolic equations and we introduce a finite difference scheme for its numerical solution. We study the behaviour of the exact solution by means of the numerical scheme. We show the positivity, the decrease and the decay to extinction of the numerical solution. Finally we report the results of the numerical tests; in these simulations we observe that the asymptotic behaviour of the reaction-diffusion system is the same as that of the associated ODE system (Kermack-McKendrick model).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/42990
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