Stability Analysis for a Discrete SIR Epidemic Model with Delay and General Nonlinear Incidence Function

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Résumé

In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, the general incidence function f must satisfy certain assumptions, under which, we establish the global stability of endemic equilibrium when R0 >1. The global stability of diseases-free equilibrium is also established when R0 ≤1. In addition we present numerical results of the continuous and discrete model of the different class according to the value of basic reproduction number R0.

Mots-clés

SIR model, discrete-time epidemic model, time delay, backward difference scheme, global stability, endemic equilibrium, disease-free equilibrium, basic reproduction number, positivity and boundedness of solutions, Lyapunov function