On the Future of HIV/AIDS in Botswana in the Presence of Drop-Outs: Insights from a Simple Mathematical Model

In response to the severe HIV/AIDS epidemic in Botswana, the Botswana government recently adopted the test and treat strategy which provides immediate treatment to people who test positive to HIV. In this paper, a deterministic HIV/AIDS model incorporating the test and treat strategy, individuals dropping out and re-enrolling to treatment is formulated and analysed. The model has two steady states, the disease free and the endemic equilibrium points. The global stabilities of the disease-free and the endemic equilibria using Lyapunov functions are established. The model is fitted to Botswana HIV/AIDS data to estimate model parameters. The numerical results and projections show that a combination of increasing enrolment and retainment to treatment reduce the disease spread but is not enough to end the disease. The results suggest the need to reduce new infections in order to end the epidemic.