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.
Highlights
In certain epidemiological modeling, the population is generally divided into three classes which are susceptible represented by S, infected individual represented by I and recovered individual represented by R
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
We have studied a discrete SIR epidemic model with general incidence
Summary
The population is generally divided into three classes which are susceptible represented by S, infected individual represented by I and recovered individual represented by R. This kind of mathematical model is noted SIR. Many authors have studied the dynamical behavior of epidemic models (see [1] [2] [3] and references therein). There are two kinds of mathematical models: The continuous-time models described by differential equations, and the discrete-time models described by difference equations. The simplest forms of these models are Ordinary Differential Equations
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