Optimal prevention of HIV-AIDS with emphasis on unprotected and unnatural canal activities: a deterministic modelling perspective

Abstract

HIV accounts for more than thirty three million death and approximately thirty eight million infected cases since it’s inception. The disease unfolds in three stages; Chronic, Acute and fully blown AIDS. Adhering to preventive protocols such as use of condoms, preventing oneself from unprotected sex and limiting one’s sexual partners could help minimize the disease spread. In this study, a deterministic model for HIV-AIDS is formulated. The equilibrium points, local and global stability of the equilibrium points, and HIV reproductive rate were determined and interpreted. The model was extended to optimal control by simulating the optimality system. This was done by incorporating the use of condoms and education of susceptible population as intervention strategies. It was established that the best and most effective control strategy was optimal education and sensitisation of susceptible population.