Abstract
The management of HIV/AIDS has evolved ever since discovering the disease in the past four decades. As a result, many countries have had to develop and revise their HIV/AIDS policies as new information on the virus, and its transmission dynamics emerged. In this research, deterministic HIV/AIDS models incorporating the test and treat policy are developed and analysed. The reproduction numbers were computed using the next-generation matrix method. The global stabilities of the equilibria using Lyapunov functions are established. Numerical simulations and results are presented. The first model has a new compartment of individuals dropping out and re-enrolling to treatment. The model has two steady states, the disease-free and the endemic equilibrium points. The numerical results and projections show that a combination of increasing enrollment and retainment to treatment reduces the disease spread but is not enough to end the disease. Next, we model the HIV/AIDS treatment policy changes tracked in three epochs. Models for each era are formulated from a ”grand” model that covers all the epochs. The grand model’s steady states are determined and analysed using the basic reproduction number, R0. The model exhibits a backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibrium when R0 < 1. The changes in the populations in each compartment are tracked as the treatment policy changed over time. Finally, projections are made to determine the possible trajectory of HIV/AIDS in Botswana. The implications of the policy changes are easily seen, and a discussion on how these changes impacted the epidemic are articulated. The numerical results have crucial impacts on how policy changes affect the trajectory of the epidemic in Botswana.
Ph.D. (Mathematics and Applied Mathematics)