Mathematical modeling and analysis of human-to-human monkeypox virus transmission with post-exposure vaccination

Monkeypox virus is a viral zoonotic disease that mostly found in a tropical area of West and central Africa. The disease outbreak occurred in 2022 affected 106 countries from all the six World Health Organization geographic regions and the outbreak accounts for the highest and unprecedented human-to-human transmission. In this paper, a new deterministic mathematical model incorporating post-exposure vaccination, pre-exposure vaccination and isolation is proposed to describe the human-to-human transmission dynamics of monkeypox virus. The analysis of the model shows that it exhibit two equilibria, which are disease free equilibrium and endemic equilibrium. However, the disease free equilibrium is proved to be both locally and globally asymptotically stable whenever the effective reproduction number is less than unity, while the endemic equilibrium is locally and globally asymptotically stable whenever the effective reproduction number is greater than unity. Some of the parameter values of the model are estimated using Nigeria 2022 monkeypox data, while some are obtained from the literature of monkeypox virus mathematical models. Optimal control system is also developed with three control strategies (public awareness campaign, post-exposure vaccination and isolation) to determine the best combination that can immensely decline the transmission or eradicate the disease. We proved that the optimal control indeed exist and we established the optimality conditions through the application of Pontryagin’s principle. The simulation result shows that post-exposure vaccination alone has rare impact in decreasing the spread of monkeypox virus while combination of two strategies (pre-exposure vaccination and isolation or post-exposure vaccination and isolation) have higher impact. In addition, the optimal control simulations show that combining public awareness campaign, post-exposure vaccination and isolation is the best to eradicate monkeypox virus in the society for insufficient vaccine that can cover the large susceptible population.