Mathematical Analysis of HIV/AIDS by Incorporating the Usage of Condoms, Prophylaxis and Antiretroval Drugs as Intervention Measures
DOI:
https://doi.org/10.5890/JAND.2027.03.011Abstract
Since the 1980s, HIV/AIDS has evolved from an acute epidemic into a manageable chronic condition, yet approximately 39 million people worldwide live with HIV, highlighting persistent gaps in epidemic control. In this research work, We develop a compartmental model of HIV/AIDS transmission incorporating pre-exposure prophylaxis (PrEP), post-exposure prophylaxis (PEP), condom usage, and antiretroviral treatment (ART). Mathematical analysis shows local asymptotic stability when the basic reproduction number $(R_{0H}) < 1$. The model exhibits backward bifurcation with imperfect prophylaxis, where endemic states persist even when $R_{0H} < 1$; this vanishes at 100% efficacy. Sensitivity analysis identified natural death rate, HIV-to-AIDS progression, contact rate, and AIDS-to-treatment progression as most influential parameters. Calibrated with South African data (2010-2023), the model predicts 28% reduction in new infections by 2033. Simulations show that high condom efficacy $(>80\%)$ combined with PrEP, PEP, and ART could reduce transmission by 75%, demonstrating the effectiveness of integrated prevention strategies.References
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