Backward bifurcation in an HIV model with two target cells

A deterministic HIV model for the transmission dynamics of HIV infection, which describes the interaction of the HIV virus and two target cells (CD4 T cells and macrophages), is proposed and analyzed. The model exhibits the phenomenon of backward bifurcation, where a locally asymptotically stable disease-free equilibrium co-exists with a locally asymptotically stable endemic equilibrium when the basic reproduction number is less than unity. This shows that bilinear incidence, which is similar to the standard incidence, can cause the backward bifurcation.