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, 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.