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has been cited by the following article:

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

  AUTHORS: Aboudramane Guiro, Dramane Ouedraogo, Harouna Ouedraogo

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

  JOURNAL NAME: Applied Mathematics, Vol.9 No.9, September 18, 2018

  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.