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

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Document pages: 16 pages

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 discretizationis one. The dynamical properties are investigated (positivity andthe boundedness of solution). By constructing the Lyapunov function, thegeneral incidence function f must satisfy certain assumptions, under which,we establish the global stability of endemic equilibrium when R0 >1. Theglobal stability of diseases-free equilibrium is also established when R0 ≤1.In addition we present numerical results of the continuous and discrete modelof the different class according to the value of basic reproduction number R0.

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