Abstract
Nations struggled to decide when and how to end COVID-19 inspired lockdowns, with sharply divergent views between those arguing for a resumption of economic activity and those arguing for continuing the lockdown in some form. We examine the choice between continuing or ending a full lockdown within a simple optimal control model that encompasses both health and economic outcomes, and pays particular attention to when need for care exceeds hospital capacity. The model shows that very different strategies can perform similarly well and even both be optimal for the same relative valuation on work and life because of the presence of a so-called Skiba threshold. Qualitatively the alternate strategies correspond to trying essentially to eradicate the virus or merely to flatten the curve so fewer people urgently need healthcare when hospitals are already filled to capacity.
Highlights
The novel SARS-CoV-2 virus has literally swept around the globe
This paper is about planning the timing of complete lockdowns in COVID-19 times
The drawback is the concurrent reduction in economic activity
Summary
The novel SARS-CoV-2 virus has literally swept around the globe. A prominent countermeasure has been to “lock down” non-essential parts of the economy to reduce contagious spread through social interaction. [6] depart from the SIR dynamics and have economic activity as a control variable Increasing this variable on the one hand raises output, but on the other hand it feeds the number of infections, raising the burden on the health care system. Calibrating their model based on the U.S situation, they suggest a lockdown of 50 days in which economic activity is reduced by two-thirds. Like us, [10] extend the SIR framework by including a state for individuals exposed to the virus but not symptomatic, and they consider limited capacity of the health system Their main result is that testing generates considerable welfare gains. Deaths from COVID-19 in the objective function can be written as x1pI þ x2 max ðf0; pI À Hmaxg; zÞ; where ξ1 is the death rate from COVID-19 of infected people who need and receive critical care, and ξ2 is the additional, incremental death rate when such individuals do not receive that care
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