STABILITY ANALYSIS OF A DELAYED FRACTIONAL
ORDER SIRS EPIDEMIC MODEL WITH
NONLINEAR INCIDENCE RATE
Mouhcine Naim1, Fouad Lahmidi2, Abdelwahed Namir3
1,2,3Department of Mathematics and Computer Science
Faculty of Sciences Ben M'sik
Hassan II University, P.O. Box 7955
Sidi Othman, Casablanca, MOROCCO

Abstract

In this paper, we study the stability of a fractional order SIRS epidemic model with nonlinear incidence rate and time delay, where the fractional derivative is defined in the Caputo sense. The delay is introduced into the model in order to modeled the incubation period. Using the stability analysis of delayed fractional order systems, we prove that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number $R_{0}<1$. Also, we show that if $R_{0}>1$, the endemic equilibrium is locally asymptotically stable.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 5
Year: 2019

DOI: 10.12732/ijam.v32i5.1

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