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As the COVID19 spreads across the world, prevention measures are becoming theessential weapons to combat the pandemic in the period of crisis. The lockdownmeasure is the most controversial one as it imposes an overwhelming impact onour economy and society. Especially when and how to enforce the lockdownmeasures are the most challenging questions considering both economic andepidemiological costs. In this paper, we extend the classic SIR model to findoptimal decision making to balance between economy and people's health duringthe outbreak of COVID-19. In our model, we intend to solve a two phasesoptimization problem: policymakers control the lockdown rate to maximize theoverall welfare of the society; people in different health statuses takedifferent decisions on their working hours and consumption to maximize theirutility. We develop a novel method to estimate parameters for the model throughvarious additional sources of data. We use the Cournot equilibrium to modelpeople's behavior and also consider the cost of death in order to leveragebetween economic and epidemic costs. The analysis of simulation resultsprovides scientific suggestions for policymakers to make critical decisions onwhen to start the lockdown and how strong it should be during the whole periodof the outbreak. Although the model is originally proposed for the COVID19pandemic, it can be generalized to address similar problems to control theoutbreak of other infectious diseases with lockdown measures.

Optimal Lockdown Policy for Covid-19: A Modelling Study