Fractional optimal control of hantavirus transmission between rodents and humans

This paper studies a fractional optimal control problem for a hantavirus transmission model involving interactions between rodent reservoirs and human populations. The model is formulated through a modified SIR–SIR structure, where both humans and rodents are divided into susceptible, infected, and recovered classes. The classical integer-order model is extended by using the Caputo fractional derivative, which captures memory and hereditary effects in the disease dynamics. Three time-dependent control variables are introduced: rodent culling, environmental sanitation, and treatment of infected humans. Positivity, boundedness, existence, and uniqueness of solutions are established to guarantee the biological and mathematical validity of the model. An optimal control problem is then formulated to minimize infected humans, infected rodents, and the costs of intervention. Necessary optimality conditions are derived using Pontryagin’s maximum principle for fractional systems. The adjoint equations, transversality conditions, and explicit characterization of the optimal controls are obtained. A numerical scheme based on the fractional Adams–Bashforth–Moulton predictor–corrector method combined with the forward–backward sweep algorithm is implemented. Several numerical scenarios are investigated, including no control, single-control strategies, and combined optimal controls. The simulations show that the combined strategy gives the strongest reduction in both infected humans and infected rodents. The results illustrate how memory-dependent dynamics can alter the predicted transmission trajectories and optimal intervention profiles. However, empirical calibration and validation using compatible human and rodent surveillance data are required before the model can be used for outbreak-specific prediction.