Mathematical modeling and optimal control analysis of the monkeypox Clade II infection dynamics under the recent cases of USA

This work presents a mathematical model with optimal control analysis of the monkeypox (mpox) Clade II dynamics, particularly in response to the recent cases reported in the USA. Initially, we develop the model and outline its key properties. We identify the equilibrium points associated with the Clade II model and analyze their asymptotic stability, demonstrating that the Clade II system is locally asymptotically stable (LAS) when the threshold quantity is less than one. We derive the endemic equilibrium point and examine its corresponding results. Considering the reported cases of Clade II in the USA, we employ a nonlinear least-squares curve-fitting method to estimate the parameters. The estimated basic reproduction number, R 0 , is 3.3282. We conduct a global sensitivity analysis to determine the parameters that most significantly affect the threshold quantity. Furthermore, we formulate an optimal control system for the Clade II virus by introducing controls such as personal protection, treatment of infected individuals, hospital care improvement, and protection from animals (e.g., animal culling). Numerical simulations are carried out for the sensitive parameters. We also simulate both the controlled and uncontrolled systems and discuss the outcomes. The results show that implementing all control measures simultaneously leads to a more significant reduction in the number of infected cases. • A novel mathematical model is developed to analyze the transmission dynamics of monkeypox (Clade II) in response to recent outbreaks in the USA. • The model demonstrates local asymptotic stability (LAS) of the disease-free equilibrium when the threshold parameter is below one. • Parameter estimation using nonlinear least squares fitting yields a basic reproduction number R 0 = 3 . 3282 . • Sensitivity analysis identifies the most influential parameters affecting disease spread and control outcomes. • Optimal control strategies involving personal protection, treatment, improved hospital care, and animal control significantly reduce the number of infections when implemented simultaneously.