Modeling the impact of biomedical prevention on HIV/AIDS transmission dynamics

The HIV/AIDS epidemic has significantly reshaped global public health priorities, prompting unprecedented investments in research, treatment programs, and prevention strategies. Despite these efforts, the disease continues to place substantial pressure on healthcare systems, particularly in resource limited settings. In this study, a deterministic dynamical system model is developed to assess the impact of key biomedical interventions on the transmission dynamics of HIV/AIDS. The well-posedness of the proposed model is established using the theory of positivity and boundedness of solutions. Analytical results show that the HIV/AIDS-free equilibrium is both locally and globally asymptotically stable whenever the effective reproduction number is less than unity ( $$\mathcal {R}_H^* < 1$$ ). Furthermore, the analysis reveals that in the presence of antiretroviral therapy (ART) defaulting, the model may exhibit a backward bifurcation. Such a result provides a plausible explanation for the sustained transmission of HIV at the national level despite achieving the effective reproduction number less than unity. In contrast, under conditions of full adherence (100%) to ART, the model exhibits a forward bifurcation, whereby the HIV/AIDS-free equilibrium is stable whenever $$\mathcal {R}_H^* < 1$$ and loses stability as $$\mathcal {R}_H^*$$ exceeds unity. Sensitivity analysis of the effective reproduction number highlights the importance of increased ART uptake across all stages of infection, together with expanded coverage of pre-exposure prophylaxis (PrEP) and post-exposure prophylaxis (PEP), as critical strategies for reducing HIV transmission. These findings are further supported by numerical simulations. A key outcome of the study indicates that ART defaulting has the greatest impact in increasing the infectious population. While promoting ART uptake remains essential, strengthening community education on sustained adherence to ART is even more critical for achieving the World Health Organization (WHO) 90-90-90 targets.