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Hopf Bifurcation Analysis In a Delayed SIR Model

Abdelhadi Abta, Hamad Talibi Alaoui, Abdelilah KADDAR

Abstract


In this paper, we analyze a delayed SIR epidemic model with saturated incidence rate. Our goal in this model is to introduce the incubation period into susceptible and infectious individuals in the incidence rate. The dynamics are studied in terms of local stability and of the description of the Hopf bifurcation, that is proven to exist as the delay (taken as a parameter of bifurcation) cross some critical value. Additionally we conclude with a numerical
illustrations.

Keywords


SIR epidemic model, delayed differential equations, Hopf bifurcation, periodic solutions.

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