MATHEMATICAL MODELING AND ANALYSIS OF THE TRANSMISSION DYNAMICS AND CONTROL STRATEGIES OF HIV/AIDS

Abstract

Acquired immunodeficiency syndrome (AIDS), caused by Human Immunodeficiency Virus (HIV), is one of the most lethal disease globally, particularly across Sub-Saharan Africa. Despite of notable advancement in prevention and treatment of HIV/AIDS, it continues to be the leading cause of death in some regions. Prevalence of the disease became higher in key populations such as men who have sex with men (MSM), people who inject drugs (PWID), sex workers and their clients, and transgender people. The thesis is based on the design and analysis of suitable compartmental deterministic mod- els for the transmission dynamics and control of HIV/AIDS in key populations. The models designed address numerous important issues related to the transmission dy- namics of HIV/AIDS, such as staged progression (i.e,,infected individuals sequentially pass through a series of stages), risk structure (i.e., risk of acquiring or transmitting infection) and sex structure. A basic risk structured model, which incorporates the back and forth movement from low to high risk group, is designed first of all. The model includes the transmis- sion of HIV by individuals in the AIDS stage of infection. Using Lyapunov function theory, in conjunction with the LaSalle Invariance Principle, the model is shown to have a globally-asymptotically stable disease-free equilibrium whenever its associated repro- duction number is less than unity. The endemic equilibrium is shown to be globally- asymptotically stable for a special case. It is further shown that the higher progression rate from high risk class to low risk class helps reducing the disease burden. Global uncertainty and sensitivity analysis of the model are carried out using a reasonable set of parameter values which singles out parameters crucial to disease dynamics. The basic risk structured model is extended to include the dynamics of two par- ticular key populations, namely sex workers and their clients. The global asymptotic stability of the disease-free equilibrium, and the local stability of the associated en- demic equilibrium are established. It is shown that if individuals in key population groups move to susceptible class with low risk in higher rate, then the transmission of the disease will be decreased. Prolonging the stay of individuals in sex workers and clients of sex workers classes in secondary infection stage decrease disease burden. Controls, namely educational campaign, HIV counseling, testing (HCT) and treatment are introduced to this model and conditions for optimal control are derived. Finally, a two-group (two-sex) model is designed to incorporate sex-structure along with risk structure. The model is shown to have a globally asymptotically stable disease-free equilibrium whenever reproduction number is less than unity and a globally- asymptotically stable endemic equilibrium whenever reproduction number is greater than unity. Disease is shown to be uniformly persistent in the population whenever reproduction number is greater than unity. Global uncertainty and sensitivity analysis of the model are performed using a reasonable set of parameter values.