Analysis of a viral disease model with saturated contact rate

A viral disease model with saturated contact rate is introduced and investigated. The model consists a host species, which is divided into two classes the susceptible and infected, and a virus, which causes a viral disease in the host and as the host induces, the infected releases more virus into the environment. Taking the virus replication rate as the bifurcating parameter, we prove that there exists a threshold value beyond which the endemic equilibrium bifurcates from the free disease one. Further increasing the value, the endemic equilibrium loses its stability, Hopf bifurcation occurs and a periodic solution arises from it. The orbital stability of the periodic orbits is analyzed by applying Poore's condition. In the last, numerical simulation of the model is employed to explain the mathematical results of this paper.