Stability analysis in a delayed SIR epidemic model with a saturated incidence rate

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 on the dynamics of SIR epidemic model. We show that if the basic reproduction number, denoted, R0, is less than unity, the diseasefree equilibrium is locally asymptotically stable. Moreover, we prove that if R0 > 1, the endemic equilibrium is locally asymptotically stable. In the end some numerical simulations are given to compare our model with existing model.