Modelling and analysis of an HIV model with control strategies and cost-effectiveness

The Human Immunodeficiency Virus (HIV) remains a significant public health concern, despite global efforts to reduce new infections and increase access to antiretroviral treatment. While pre-exposure prophylaxis (PrEP) has shown promise in reducing new infections, its overall effectiveness is hindered by challenges in adherence. In this paper, a novel model was proposed. The basic properties of the model were established and the reproduction number for the model without control was computed. We conducted a sensitivity analysis to highlight the need for optimal control analysis and hence proposed an optimal control model that incorporates PrEP, condom use, and antiretroviral treatment to capture the dynamics of HIV transmission. The existence of the optimal control was mathematically proven and Pontryagin's maximum principle was employed to establish the necessary optimal control conditions. Utilizing demographic and epidemiological parameters specific to South Africa, we conducted numerical simulations. The results demonstrate the community-level benefits of implementing a combination of control measures for HIV reduction. Additionally, a cost-effectiveness analysis was performed to determine the most effective and economically viable control strategies. We anticipate that the findings from this analysis will provide valuable insights for policymakers in designing effective HIV control programmes.