How long should the COVID-19 lockdown continue?

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.

The optimal lockdown intensity for COVID-19

“…Of course the primary consideration is health which we model as in an earlier paper, see Caulkins et al (2020) . Deaths dominate health costs because the duration of sickness is relatively short compared with diseases such as cancer, let alone dementia.…”

“…Deaths dominate health costs because the duration of sickness is relatively short compared with diseases such as cancer, let alone dementia. A contribution of Caulkins et al (2020) that we also include here is making the risk of death for an infected individual depend on the population-prevalence because the healthcare system can become swamped. In particular, if the number of infected individuals times the probability that an infected person needs critical care is less than the healthcare system’s capacity ( ) then the death rate has one value ( ); otherwise, for those who cannot receive critical care, it gets bumped up by an additional increment ( ).…”

“…In particular, if the number of infected individuals times the probability that an infected person needs critical care is less than the healthcare system’s capacity ( ) then the death rate has one value ( ); otherwise, for those who cannot receive critical care, it gets bumped up by an additional increment ( ). Implementing that literally would require a function with a discontinuous derivative, but as Caulkins et al (2020) explain, it is possible to find a continuously differentiable function which very closely approximates it. Hence, the health care cost component of the objective function is: with The label “ ” with a subscript is meant to denote a smoothed version of the maximum function.…”

“…The present paper preserves ( Caulkins et al, 2020 ) modeling of intensive care capacity and extends it by allowing for multiple lockdowns with different intensities and lengths. We also explicitly model “lockdown fatigue” by an additional state variable that accumulates the intensity and length of the lockdown.…”

“… Caulkins et al (2020) adds to this literature by considering the limited capacity constraint of intensive care units within the health care system. If the number of infected people needing intensive care exceeds the constraint the death rate of these patients increases relative to similar individuals who are able to receive appropriate care.…”