Can full vaccination and treatment suppress COVID-19–HIV/AIDS co-infection? Insights from fractional-order modeling via Atangana–Baleanu operator

Despite extensive research on COVID-19–HIV/AIDS co-infection, the combined effects of full vaccination and treatment within a fractional-order dynamic framework remain largely unexplored. In this study, a novel fractional-order model for COVID-19–HIV/AIDS co-infection is developed using the Atangana–Baleanu derivative in the Caputo sense, capturing the memory and hereditary properties inherent in co-infection dynamics. The model incorporates both the first- and second-dose vaccination rates alongside co-infection treatment programs, providing a more comprehensive representation of disease control strategies. A numerical scheme based on the Toufik–Atangana two-step Lagrange interpolation and the fundamental theorem of fractional calculus is employed to obtain approximate solutions. Model parameters were estimated using real epidemiological data from New Delhi, India, to ensure data-driven realism. Simulation results reveal that lower fractional orders amplify memory effects, prolonging infection persistence and delaying eradication, while moderate full vaccination coverage and enhanced treatment rates substantially reduce the effective COVID-19 reproduction number and accelerate recovery from co-infection. These results highlight the critical role of fractional-order dynamics in delayed immune responses and cumulative treatment effects, which are often overlooked in integer-order models. The proposed framework provides a powerful analytical tool for evaluating vaccination and treatment policies in immunocompromised populations with multiple interacting infections.