Dynamics and optimal control of fractional-order monkeypox epidemic model with social distancing habits and public awareness

In this article, we propose a fractional-order monkeypox epidemic model incorporating social distancing habits and public awareness. The model includes the addition of a protected compartment and a saturated transmission rate. We implement a power rescaling for the parameters of the proposed model to ensure dimensional consistency. We have investigated the existence, uniqueness, nonnegativity, and boundedness of the solution. The model features monkeypox-free, human-endemic, and endemic equilibrium points, which depend on the order of derivative. The existence and stability of each equilibrium point have been analyzed locally and globally, depending on the basic reproduction number. Moreover, the basic reproduction number of the model also depends on the order of derivative. We carried out a case study using real data showing that the fractional-order model performs better than the first-order model in calibration and forecasting. Numerical simulations confirm the stability properties of each equilibrium point with respect to the specified parameter values. Numerical simulations also demonstrate that the social distancing habits can reduce monkeypox cases in the early stages, but do not significantly alter the basic reproduction number. Meanwhile, public awareness can substantially modify the basic reproduction number, shifting the endemic condition towards a disease-free state, although its impact on case reduction in the early period is not significant. We also implemented optimal control strategies for vector culling and vaccination in the proposed model. We have solved the optimal control problem, and the simulation results show that the combination of both controls yields the minimum cost with better effectiveness compared to the controls implemented separately.