Effects of treatment and prevalence-dependent recruitment on the dynamics of a fatal disease

This paper studies models for the sexual transmission of HIV/AIDS that incorporate changes in behaviour and the effects associated with HIV treatment. The recruitment rate into the core is assumed to be a function of the prevalence of the disease within the core, and it may trigger the existence of periodic solutions through Hopf bifurcations, provided that there is at least a weak demographic interaction with the noncore. The recruitment function is set up for two cases: dependence on the total proportion of infectious individuals and dependence on the proportion of treated infectious individuals only. In the general model, numerical evidence suggests that both cases may produce periodic solutions when the perception of the risk of joining the core group is sufficiently high. Two limiting cases are also studied: when the growth rate of the core and noncore groups are essentially the same, and when treatment has no effect on the transmission rate of infected individuals.