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Stability analysis in a delayed SIR epidemic model with a saturated incidence rate. (English) Zbl 1227.34084

Summary: We formulate a delayed SIR epidemic model by introducing a latent period into susceptible and infectious individuals in incidence rate. This new reformulation provides a reasonable role of incubation period for the dynamics of the SIR epidemic model. We show that if the basic reproduction number, denoted by \(R_0\), is less than unity, the disease-free equilibrium is locally asymptotically stable. Moreover, we prove that if \(R_0>1\), the endemic equilibrium is locally asymptotically stable. In the end, some numerical simulations are given to compare our model with existing model.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K13 Periodic solutions to functional-differential equations
34K18 Bifurcation theory of functional-differential equations
34K20 Stability theory of functional-differential equations
92D30 Epidemiology
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