Design of Monkeypox Virus Spread Control in Humans Using Pontryagin Minimum Principle

Hanafi, Lukman (Mathematics Department Institut Teknologi Sepuluh Nopember Surabaya)
Mardlijah, Mardlijah (Mathematics Department Institut Teknologi Sepuluh Nopember Surabaya)
Utomo, Daryono Budi (Mathematics Department Institut Teknologi Sepuluh Nopember Surabaya)
Wahyudi, Suhud (Mathematics Department Institut Teknologi Sepuluh Nopember Surabaya)
Sha-brina, Alya Nur (Mathematics Department Institut Teknologi Sepuluh Nopember Surabaya)

International Journal of Computing Science and Applied Mathematics
Vol 10, No 2 (2024)

Monkeypox is a contagious disease caused by a virus. In Africa, monkeypox results in death in 1 out of 10 infected individuals. The Food and Drug Administration in the United States recommends vaccination as a preventive measure against monkeypox virus. If infected, the World Health Organization (WHO) advises quarantine to prevent further transmission to others. This research develops a mathematical model known as SIR (Susceptible-Infected-Recovered) for the spread of monkeypox virus, incorporating vaccination and quarantine as control measures. The SIR model utilized is based on an existing model and follows the conditions of monkeypox spread in Nigeria, represented as a system of nonlinear differential equations. Optimal control is determined using the Pontryagin Minimum Principle and simulated using the fourth-order forward-backward sweep Runge-Kutta method to assess the level of monkeypox infection before and after implementing control measures. Based on the simulation results, it is concluded that the application of control measures can reduce the population of infected monkeys by 70% and infected humans by 59%.