Optimal Lockdown Decisions of the Stochastic SIR Model with the Allocation Medical Resources (Financial Modeling and Analysis)

Abstract

We consider the optimal timing (start and end) of lockdowns during the COVID-19 pandemic to minimize the expected total cost, which includes the opportunity cost of economic activities and the disease burden in medical facilities, based on the stochastic SIR model. The model incorporates uncertainty around the contact rate and the choice of the medical resource level. The major differences from the standard SIR model are as follows: (i) the model takes into account two types of deaths, those due to infectious and non-infectious diseases; (ii) it allows decision-makers to make a sequence of decisions regarding lockdown during the pandemic; (iii) the model is formulated as a combination of optimal stopping and a stochastic control problem; (iv) it is shown, under the assumption of linear variety, that there exists a simple optimal lockdown policy and an optimal investment level in medical resources; and (v) these optimal policies depend not only on the parameters of the infectious process but also on the contact rate, the number of susceptible individuals remaining at the decision epoch, and the marginal cost with respect to the infection rate.