Fractional‐Order Modeling and Parameter Estimation of Schistosomiasis Transmission With Environmental Factors and Concomitant Immunity

Schistosomiasis remains a major public health burden in endemic regions where repeated contact with cercariae‐contaminated freshwater sustains transmission. This study proposes a fractional‐order schistosomiasis model based on the Atangana–Baleanu–Caputo (ABC) derivative with a Mittag‐Leffler kernel. The model includes susceptible, exposed, and infected humans; a concomitant‐immunity class; infected nonhuman mammals; and the concentration of cercariae in the aquatic environment. Using fixed‐point theory, we prove the existence and uniqueness of solutions, while Ulam–Hyers stability is established to assess the robustness of the system. The disease‐free equilibrium is obtained, and the basic reproduction number is derived using the next‐generation matrix method. A direct comparison between the ABC fractional‐order model and its integer‐order counterpart is also performed to demonstrate the effect of memory on the transient disease dynamics. The numerical results show that the fractional order has a significant effect on the transient behavior of the disease: smaller fractional orders, slow the evolution of the system, whereas values closer to one accelerate the growth of infected and environmental compartments. In addition, a synthetic‐data parameter‐estimation study is carried out to evaluate the recovery of key parameters and initial conditions. Overall, the results highlight the role of fractional memory in describing schistosomiasis transmission under environmental exposure, concomitant immunity, and mammalian reservoir effects.