Abstract

THE EFFECT OF FRACTIONAL-ORDERALPHA, ?,ON THE BEHAVIOR OF DYNAMICAL SYSTEMS FOR EPIDEMIC MODEL

A. E. Owoyemi, S. E. Olowo, D. Y. Idris, E. A. Olujosun, M. N. Umunagbu, I. Abdulmalik, W. O. Okedokun ,M. O, Aigbavboa,U. Dahiru And S

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Abstract Recently, many deterministic mathematical model had been extended to fractional model with some fractional differential equations. It was believed that these fractional models are more realistic to represent the daily life phenomena than its integral?order counterpart. The main focus of this paper is to extend the model of asusceptible-infected-refractory(SIR) epidemic model to fractional model. More specifically, the fractional SIR epidemic model with sub-optimal immunity, nonlinear incidence and saturated recovery rate was discussed. The fractional ordinary differential equations were defined in the sense of the Caputo derivative. Existence, equilibrium points and the stability analysis for the fractional models were analyzed. We applied Adams-type predictor-corrector method to the numerical solutions of the models. Maple 18 is used as the software platform. The result also confirmed that choosing appropriate values of the fractional ? ? [0, 1] increase the stability region of the equilibrium points. Keywords: Sub-optimal immunity, nonlinear incidence, saturated recovery rate, fractional-order, stability analysis.

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