An optimal control model for monkeypox transmission dynamics with vaccination and immunity loss following recovery

The viral illness known as monkeypox causes symptoms such a rash that can appear on the hands, feet, chest, face, and lips or near the genitalia. This study presents a mathematical model for the kinetics of monkeypox transmission with vaccination and immunity loss following recovery. The theories of positivity and boundedness are used to analyze the model’s well-posedness. The next generation matrix is used to determine the model’s basic reproduction number. The model’s equilibrium points are discovered. We demonstrate that the disease-free equilibrium was locally asymptotically stable. The center manifold theory is used to establish the bifurcation analysis. The impact of the parameters related to the fundamental reproduction number $R_0$ is investigated using the normalized forward sensitivity index. In addition, the model is expanded to incorporate time-dependent management of preventing interaction with contaminated rodents, avoiding contact with contaminated people, wearing personal protective equipment, and reducing rodent populations by utilizing an integrated pest management strategy. The model’s qualitative analysis is supported by numerical simulation.