Stochastic modeling of an HIV/AIDS epidemic with treatment

Abstract

The HIV/AIDS epidemic continues to be among the most devastating diseases in human history despite the new scientific advances and serious public health interventions. The greatest burden of HIV/AIDS is still in sub-Saharan Africa, and within this specific region, women are severely affected. Despite an increase in prevention interventions, including such as ARV treatment and pre-exposure prophylaxis (PrEP), behavioural change remains a key role in the transmission of HIV/AIDS. In this thesis, we investigate several related models for the population dynamics of HIV/AIDS epidemic model with treatment. We start off with a four compartmental HIV deterministic model with stages of HIV infection and with inflow of HIV infectives. Thereafter, we impose stochastic perturbations on the underlying HIV/AIDS deterministic model without inflow of infectives. For this version of HIV stochastic model, we prove global existence and positivity of solutions to the HIV/AIDS-perturbed model. Some useful properties such as boundedness property, stochastic permanence property and asymptotic stability have been derived.