A novel model for monkeypox disease: System analysis and optimal preventive strategies

Abstract

Monkeypox is an infectious disease caused by the monkeypox virus, which belongs to the Poxviridae virus family and the Orthopoxvirus genus. Although initially endemic in Africa, it has recently become a global threat with cases worldwide. Hence, this study aims to propose a new monkeypox transmission model that represents the interaction between the infected human and infected rodent populations. To predict the future of the disease, the reproduction number is determined and the sensitivity of this threshold parameter to the model parameters is analyzed. Then, the stability of the model is discussed at monkeypox-free and viral equilibrium points. Furthermore, according to the sensitivity analysis, control variables are adapted to the model as the optimal prevention and treatment strategies to reduce the spread of the disease. For this purpose, the existence of optimal control is first ensured. The aim of the proposed optimal control problem is to minimize both the treatment and prevention costs, and the number of infected individuals. Optimality conditions are acquired using Pontryagin’s Maximum Principle. To arrive the optimal solutions, fourth-order Runge–Kutta numerical method combined with the forward-backward sweep iteration is used. Numerical simulations clearly show how necessary and successful the proposed combined control strategy is in preventing the disease from becoming epidemic.