Article

Global stability for the continuous and discrete SIS-diffusion epidemiological models

Published in: Quaestiones Mathematicae
Volume 40 , issue 2 , 2017 , pages: 161–176

DOI: 10.2989/16073606.2017.1283369

Author(s): J.M.-S. Lubuma Department of Mathematics and Applied Mathematics, South Africa , Y.A. Terefe Department of Mathematics and Applied Mathematics, South Africa

Keywords: 37N25 , 37N30 , 65C20 , 92B05 , 37N25 , 37N30 , 65C20 , 92B05

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Abstract

A susceptible-infectious-susceptible reaction-diffusion equation is used to model the spatial spread of a disease. It is shown that the disease-free equilibrium (DFE) is globally asymptotically stable (GAS) when the basic reproduction number is less than or equal to 1 and unstable when it is greater than 1. In the latter case, there exists an endemic equilibrium (EE) which is GAS. We construct nonstandard finite difference (NSFD) schemes which theoretically and computationally replicate the stability properties of the equilibria.

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