Mathematical Analysis of a Malaria and HIV/AIDS Co-infection Model Incorporating Vaccination, Pre-Exposure Prophylaxis, and Anti-Retroviral Treatment

In sub-Saharan Africa, malaria and HIV/AIDS impose a devastating dual burden. Their biological synergy—acute malaria temporarily raising HIV viral load and HIV-driven immunosuppression amplifying malaria severity—accelerates morbidity and mortality beyond what either disease causes alone. We develop and evaluate a deterministic 19-compartment malaria–HIV/AIDS co-infection model (16 human compartments coupled to a 3-compartment Anopheles vector framework), including RTS, S/AS01 vaccination, HIV pre-exposure and post-exposure prophylaxis, and antiretroviral therapy, in order to quantify and manage this compounded threat. A sharp disease-free stability threshold is governed by the basic reproduction number [Formula: see text] = max([Formula: see text]), which is obtained using the next-generation matrix method. According to sensitivity analysis, the main factors influencing the spread of HIV and malaria are behavioral prevention and mosquito biting rates, respectively. Simulations under three fractional-order operators—Caputo, Caputo–Fabrizio, and Atangana–Baleanu–Caputo—show that concurrently increasing RTS, S/AS01 vaccination, expanding ART coverage, and boosting condom compliance drives [Formula: see text], removing endemic equilibria for both pathogens and confirming integrated intervention as the best public health approach in co-endemic settings.