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

摘要

We formulate a delayed SIR epidemic model by introducing a latent period intosusceptible, and infectious individuals in incidence rate. This new reformulation providesa reasonable role of incubation period on the dynamics of SIR epidemic model. Weshow that if the basic reproduction number, denoted, R0, is less than unity, the disease-free equilibrium is locally asymptotically stable. Moreover, we prove that if R0> 1,the endemic equilibrium is locally asymptotically stable. In the end some numericalsimulations are given to compare our model with existing model