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.