On the bifurcations and multiple endemic states of a single strain HIV model

The dynamics of a single strain HIV model is studied. The basic reproduction number R 0 used as a bifurcation parameter shows that the system undergoes transcritical and saddle-node bifurcations. The usual threshold unit value of R 0 does not completely determine the eradication of the disease in an HIV infected person. In particular, a sub-threshold value R c is established which determines the system’s number of endemic states: multiple if R c < R 0 < 1, only one if R c = R 0 = 1, and none if R 0 < R c < 1.