Mathematical Modelling and Analyzing the Dynamics of Condom Efficacy and Compliance in the Spread of HIV/AIDS

The study involves a mathematical analysis of condom efficacy and compliance in the transmission of HIV/AIDS. It explores how condom use impacts the prevention of HIV/AIDS and considers other epidemiological factors affecting the progression from HIV to full-blown AIDS. The model's existence and uniqueness of solution are established, with a focus on the basic reproduction number, representing the average new infections caused by an infected individual. The analysis reveals that the disease-free equilibrium is stable when the basic reproduction number is below unity i.e., but becomes endemic otherwise, i.e.. Sensitivity analysis indicates parameters with positive values increase the reproduction number, emphasizing that the effective contact rate should not exceed 0.22 to avoid the endemic stage. Numerical simulations using MAPLE 18 software demonstrate that condom compliance reduces the dynamic spread of HIV, and targeted immunity boost controls the viral load.