Optimal interventions of infectious disease

Abstract

The recent outbreak of novel coronavirus has highlighted the need for a benefit‐cost framework to guide unconventional public health interventions aimed at reducing close contact between infected and susceptible individuals. In this paper, we propose an optimal control problem for an infectious disease model, wherein the social planner can control the transmission rate by implementing or lifting lockdown measures. The objective is to minimize total costs, which comprise infection costs, as well as fixed and variable costs associated with lockdown measures. We establish conditions concerning model primitives that guarantee the existence of a straightforward optimal policy. The policy specifies two switching points , whereby the social planner institutes a lockdown when the percentage of infected individuals exceeds , and reopens the economy when the percentage of infected individuals drops below . We subsequently extend the model to cases where the social planner may implement multiple lockdown levels. Finally, numerical studies are conducted to gain additional insights into the value of these controls.