Effects of density of infected population to the spreading of HIV epidemic in communities

We present a dynamical model for the spread of HIV in a finite discrete population of size [Formula: see text] represented by the set [Formula: see text]. The model takes into account the structure of the sexual network, the density of infected population in each individual’s sexual partners, and a reasonable amount of the influence of noninfectious HIV positive individuals on HIV infectious partners which may occur in communities. In our analytic results, we give a precise epidemic threshold which, together with certain network properties, is then used to analyse and investigate the existence of epidemic and stability in the HIV spreading dynamics. Our results reproduce common observed patterns in the dynamics of HIV spreading in communities.