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

Aboudramane  Guiro; Dramane  Ouedraogo; Harouna  Ouedraogo

doi:10.4236/am.2018.99070

Aboudramane Guiro^*, Dramane Ouedraogo, Harouna Ouedraogo

Abstract:

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.

Keywords: Discrete Model, Delay, Lyapunov Functional, Nonlinear Incidence, Backward Difference Scheme, Local Stability, Global Stability

Cite this paper: Guiro, A. , Ouedraogo, D. and Ouedraogo, H. (2018) Stability Analysis for a Discrete SIR Epidemic Model with Delay and General Nonlinear Incidence Function. Applied Mathematics, 9, 1039-1054. doi: 10.4236/am.2018.99070.

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