Optimal Control Strategies on Mobility for Preventing COVID-19 Transmission: A study with A Three-Patch Compartmental Model

Abstract

Human mobility can be identified as one of the main factors that directly affect the spread of COVID-19. Accordingly, human mobility must be controlled in a proper way to deficit the spread of COVID-19 as the economy of a country depends on human mobility. Nevertheless, due to the lack of proper management of the lockdown restrictions, the economy of many countries has already suffered a severe decline. In this research, a compartmental model (SIR) has been presented using optimal control theory to deficit the spread of COVID-19. Thus, the districts of Sri Lanka were divided into three regions (three-patch), and two control variables, were used to control the normal human mobility within the region and between the region. Also, when designing the cost function, two competing factors which deficit the spread of COVID-19 and save the country's economy were considered. Furthermore, optimal solutions were obtained using the Pontryagin's maximum principle and the data related to the spread of COVID-19 in Sri Lanka from April 15 to May 15, 2021, have been used here. In this research, a lockdown policy has been mainly focused on formally imposing and removing lockdown restrictions to compromise both the competing factors of economic security and control the spread of disease. Based on the results, a clear idea could be obtained about the time limits that should be imposed lockdown restrictions within the region and between the regions. Consequently, it was apparent that starting the systematic removal of the lockdown limits within the regions and between the regions are approximately equal. Furthermore, effective reproductive number are used to check the spread of COVID-19. Hence, it can be assumed that the spread of disease is less when mobility controls are activated. The results which were obtained here can be used not only for COVID-19 but for any pandemic and endemic.