Investigating the dynamics of a novel fractional-order monkeypox epidemic model with optimal control

In this paper, a novel fractional-order monkeypox epidemic model is introduced, where fractional-order derivatives in the sense of Caputo are applied to achieve more realistic results for the proposed nonlinear model. The newly developed model, which models the transmission and spread of monkeypox across the interacting populations of humans and rodents, is controlled by a 14-dimensional system of fractional-order differential equations. To comply with empirical and reported observations, the state variables of the proposed model are categorized into three main groups of state variables: the population who are at high risk of being infected, people with low infection probability, and finally, rodents who can carry and transmit the virus. The high-risk group represents individuals who might be more vulnerable to the virus due to their habits, workplace, or hygienic behaviors. The existence, uniqueness, non-negativity, and boundedness of the solution to the proposed model are proved. The next-generation matrix approach is used to determine the control monkeypox reproduction number, R₀, and the equilibrium points for the proposed model are obtained. The effect of the main parameters in the model is thoroughly investigated to provide new insight into the new dynamics of the model. The region of stability of the disease-free points (DFE) is obtained in the space of parameters, and the effect of the parameters is examined. In addition, the optimal control strategy is applied to the model to provide insight into some prevention control to stop the disease from spreading and to provide new control strategies during the monkeypox outbreak. Numerical simulations are performed to validate the theoretical results of the different optimal control strategies.