Dynamics of an SIR epidemic model incorporating time delay and convex incidence rate

In this paper, dynamical behaviors including stability and Hopf bifurcation of a delayed SIR epidemic model with convex incidence rate are examined. We first discuss the existence of Hopf bifurcation. Subsequently, direction and stability of Hopf bifurcation are investigated. Moreover, length of the time delay which can retain stability of the proposed model has been appraised. Specially, global exponential stability is studied. Finally, numerical simulations are carried out with the suitable choices of parameters in the prosed model.