Stability analysis and Hopf bifurcation of a fractional order HIV model with saturated incidence rate and time delay

In this paper, a fractional order HIV model with saturated incidence rate and time delay is proposed and analyzed. Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the stability of two equilibriums are obtained. Thirdly, by using time delay as the bifurcation parameter, it is found that Hopf bifurcation may occur when the time delay passes through a sequence of critical values. After that, some numerical simulations are performed to verify the theoretical results. Finally, some discussions and conclusions are listed.