| Summary: | In this study, a fractional-order monkeypox epidemic model with different memory effects between humans and rodents is considered. The proposed model involves six classes of human populations (susceptible, exposed, infected, quarantined, hospitalized, and recovered) and three classes of rodent populations (susceptible, exposed, and infected). The equilibrium points of the model are disease-free, human-endemic, and endemic. The model has basic reproduction numbers of humans and rodents denoted R0h and R0r, respectively. The disease-free equilibrium always exists and is locally asymptotically stable if maxR0h,R0r<1. The human-endemic equilibrium point exists and is locally asymptotically stable if R0r<1. The endemic equilibrium point exists and is locally asymptotically stable if R0r>1. This research aims to study the optimal control of the model with vaccination and culling. We have applied the vaccination control to the human population and the culling control to the rodent population. The optimal control is obtained by minimizing the number of infected humans, the number of infected rodents, and the implementation cost of the controls. This minimization problem has been solved analytically using the modified Pontryagin’s minimum principle. We have performed the numerical simulation of optimal control by implementing the modified forward–backward sweep method and setting three strategies: vaccination, culling, and both controls. Based on numerical simulations, the optimal control of both controls is generally the best strategy, followed by culling only and vaccination only, respectively.
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