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J. P. Caulkins, D. Grass, G. Feichtinger, R.F. Hartl, P.M. Kort, A. Fürnkranz-Prskawetz, A. Seidl, S. Wrzaczek:
"The optimal lockdown intensity for COVID-19";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2020-11 (2020), 11; 29 S.

One of the principal ways nations are responding to the COVID-19 pandemic is by lockingdown portions of their economies to reduce infectious spread. This is expensive in terms oflost jobs, lost economic productivity, and lost freedoms. So it is of interest to ask: What isthe optimal intensity with which to lockdown, and how should that intensity vary dynamicallyover the course of an epidemic? This paper explores such questions with an optimal controlmodel that recognizes the particular risks when infection rates surge beyond the healthcaresystem´s capacity to deliver appropriate care. The analysis shows that four broad strategies canbe optimal, ranging from brief lockdowns that only "smooth the curve" to sustained lockdownsthat prevent infections from spiking beyond the healthcare system´s capacity. Within this model,it can be optimal to have two separate periods of locking down, so returning to a lockdown afterinitial restrictions have been lifted is not necessarily a sign of failure. Relatively small changesin judgments about how to balance health and economic harms can alter dramatically whichstrategy is optimal. Indeed, there are constellations of parameters for which two or even three ofthese distinct strategies can all be optimal for the same set of initial conditions; these correspondto so-called triple Skiba points. The performance of trajectories can be highly nonlinear in thestate variables, such that for various timest, the optimal unemployment rate could be low,medium, or high, but not anywhere in between. These complex dynamics emerge naturally from modeling the COVID-19 epidemic and suggest a degree of humility in policy debates.Even people who share a common understanding of the problem´s economics and epidemiologycan prefer dramatically different policies. Conversely, favoring very different policies is notevidence that there are fundamental disagreements.

COVID-19, Lockdown, Skiba threshold, SIR model, optimal control

https://publik.tuwien.ac.at/files/publik_289937.pdf