Abstract
This paper investigates various epidemiological aspects of HIV/AIDS through a fractional-order mathematical model, emphasizing the role of treatment in the disease's transmission dynamics. Given the ongoing global impact of HIV/AIDS, with millions of people affected and significant mortality rates, understanding the complexities of its transmission and control is crucial for effective public health strategies. We establish conditions for the existence and uniqueness of the model’s solutions within the fractional framework and perform a stability analysis of the endemic equilibrium using the Lyapunov function method. Numerical simulations, executed via the fractional Adams–Bashforth–Moulton method, demonstrate the effects of model parameters and fractional-order values on HIV/AIDS dynamics and control. Additional simulations employing surface and contour plots reveal that higher contact rates and reduced treatment efficacy correlate with increased HIV/AIDS prevalence. Our findings suggest that optimizing treatment strategies can significantly lower the prevalence of HIV/AIDS within the population, ultimately contributing to enhanced health outcomes and resource allocation in combating this critical public health issue.
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