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.


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