<b>Fractional-Order Mathematical Modeling of HIV/AIDS Transmission Dynamics via a Generalized Adams–Bashforth–Moulton Numerical Scheme</b>

Abstract

HIV/AIDS remains one of the major global public health challenges due to its high transmission rate, long-term health complications, and socio-economic impact on affected populations. Despite several intervention strategies, the disease continues to spread, particularly in regions with inadequate access to treatment and preventive measures. Motivated by the need to better understand the transmission dynamics of HIV/AIDS and the impact of treatment strategies, this paper focuses on the dynamics of HIV/AIDS transmission using a fractional-order mathematical model to assess the effect of treatment and contact rates on HIV/AIDS. The model presents the existence and uniqueness of the solution in the fractional-order sense, demonstrating the well-posedness of the model. The model's stability is analysed to understand the dynamics of the disease, including the basic reproduction number. These findings show treatment rates of exposed, asymptomatic, and symptomatic individuals play a critical role in reducing the reproduction number below one, implying control of the disease, whereas contact rates increase disease transmission and maintain the disease's presence. Sensitivity and simulation analyses show that transmission-related parameters have a positive impact on disease transmission, while treatment-related parameters have a negative sensitivity, leading to a reduction in the disease burden. The dynamics of population states for different treatment and contact rates are discussed using the fractional Adams–Bashforth–Moulton numerical scheme. Further contour and surface plots reveal that increased treatment and lower contact rates result in a significant reduction in the HIV/AIDS incidence, while poor control measures and increased contact rates increase the infection. The results highlight that early treatment of exposed individuals and treatment of infected individuals (asymptomatic and symptomatic) are key to reducing the disease burden. In summary, the study underlines the need for effective control measures incorporating treatment expansion and reduction in transmission pathways for the successful control and possible eradication of HIV/AIDS in the population.