Stability analysis in a delayed SIR epidemic model with a saturated incidence rate. (English) Zbl 1227.34084

Kaddar, A.

Nonlinear Anal., Model. Control 15, No. 3, 299-306 (2010).

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.

MSC:

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

Keywords:

SIR epidemic model; delayed differential equations; Hopf bifurcation; periodic solutions