An Optimal Control Analysis of the MERS-CoV Outbreak in South Korea

Abstract

MERS-CoV is a respiratory disease that originated in the Middle East. This disease is caused by a novel coronavirus which transmits from Dromedary camels to humans, then passed on to other humans through direct contact or droplets. Said to be the biggest to occur outside of Middle East with 186 cases, the outbreak in South Korea should be discussed further. By going through the chain of transmission, it was found that 44\% of the infected individuals were exposed to the virus in the healthcare facilities' environment. To reduce the risk of exposure to the virus, several efforts have been made such as restricting healthcare facilities visitors and increasing the number of isolated individuals in hospitals. The previous study has developed a mathematical model for the outbreak in South Korea and estimated transmission rates from the data provided by the government. In this study, both efforts will be added as control variables to form an optimal control problem to minimize the number of infected individuals and the costs incurred. The optimal control will be obtained using the Pontryagin maximum principle, then simulated using the fourth-order Runge-Kutta forward-backward sweep method for two scenarios to see the effectiveness of both controls. The simulation showed that restricting health facilities visitors to limit the chance of exposure was the most effective strategy to control the MERS-CoV outbreak in South Korea.