Discrete Fractional Order SIR Epidemic Model of Childhood Diseases with Constant Vaccination and it’s Stability

A. George Maria Selvam
Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635 601, Vellore District, Tamil Nadu, India , IN

D. Abraham Vianny
Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635 601, Vellore District, Tamil Nadu, India , IN

Keywords: fractional order, SIR model, stability, discretization process

Abstract

In this paper, we propose to study an epidemic model of childhood disease in a 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 is obtained via next generation matrix method. Time plots and phase portraits are analyzed under suitable conditions. Numerical examples are used to verify the stability results.

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