On the almost sure convergence of a stochastic process in a class of nonlinear multi-population behavioral models for HIV/AIDS with delayed ART treatment

The success in reducing global HIV prevalence rates is attributed to control measures like information and education campaigns (IECs), antiretroviral therapy (ART), and national, multinational and multilateral support providing official developmental assistance (ODAs) to combat HIV. A class of stochastic nonlinear multi-population behavioral HIV/AIDS models is studied, where behavioral change is inspired by the IECs safe sex education. Exponential almost sure stability analysis of the model is conducted, and the results are employed to determine the impacts of the supply of ODAs, IECs, early treatment and poverty rates on the epidemic. The behavioral change and the noise induced basic reproduction numbers are obtained.