Stability in a fractional order SIR epidemic model of childhood diseases with discretization

Abstract

In this paper, we propose to study the SIR epidemic model of childhood disease in human population. Fractional order SIR epidemic model is considered and its discrete form is obtained. Local asymptotic stability of disease free equilibrium and endemic equilibrium points are discussed and the basic reproduction number R0 is obtained via next generation matrix method. Time series plots, phase portraits, bifurcation diagram and sensitive dependence on initial condions are analyzed under suitable conditions. Numerical examples are used to verify the results.