Dynamic Analysis of an Sir Epidemic Model with Nonlinear Incidence Rate and Double Delays

In this paper, an SIR epidemic model with nonlinear incidence rate and double delays due to the force of infection and temporary immunity period is investigated. The existence and stability of the possible equilibria are examined in terms of a certain threshold condition R0, the basic reproduction number. Based on some comparison arguments, sharp threshold conditions which are necessary for the global stability of the equilibrium point of the model are obtained. By analyzing the corresponding characteristic equations, the dynamical behavior of the endemic equilibrium is shown from the point of view of stability switches aspects.Moreover, numerical simulations are given to support the theoretical analysis.