Modeling and stability analysis of the transmission dynamics of Monkeypox with control intervention

Abstract

Monkeypox is a deadly disease from the Orthopox family. The paper explores a nonlinear trend in the dynamics of Monkeypox propagation. In this model, we include vaccination, treatment, and level of awareness as the main parameters of the propagation of Monkeypox. We also include the quarantined infected individuals with severe complications in the Monkeypox dynamics. We show the boundedness and positivity of the model and also demonstrate the stability of the model using the Banach fixed point theory and the Picard successive approximation method to ensure that it is meaningful mathematically and epidemiologically. We obtain the unique solution of the model under appropriate conditions. This work finds three equilibrium points: Monkeypox free, Rodents free, and endemic. We show the local stability of monkeypox free equilibria and rodent-free endemic equilibria through reproduction number. Furthermore, Dulac’s function technique demonstrates the global stability of endemic equilibrium. We show the transformation from endemic equilibria to Monkeypox-free equilibria via rodent-free. We also obtain the condition of transcritical bifurcation. We analyze the system’s dynamic behavior to develop efficient infection control strategies. We find that if we increase awareness, vaccination, treatment, and quarantine rates, we effectively control the transmission. The model is connected with a continuous model using an ordinary differential equation. We examine the complex dynamics of Monkeypox infection under diverse system input factors through numerical simulation of the proposed model with variable input parameters in reducing Monkeypox. We present the theory of Monkeypox disease control in humankind as an application in real-world problems. The work can be helpful in the vector-borne disease control system.