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. 2023 Apr 15:1-28.
doi: 10.1007/s00199-023-01493-1. Online ahead of print.

A simple planning problem for COVID-19 lockdown: a dynamic programming approach

Alessandro Calvia  1 , Fausto Gozzi  1 , Francesco Lippi  1   2 , Giovanni Zanco  3
Affiliations

A simple planning problem for COVID-19 lockdown: a dynamic programming approach

Alessandro Calvia et al. Econ Theory. .

Abstract

A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach.

Keywords: Controlled SIRD model; Optimal control with state space constraints; Optimal lockdown policies; Optimality conditions; Viscosity solutions.

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Conflict of interest statement

Conflict of interestThe authors have no competing interests to declare that are relevant to the content of this article.

References

    1. Acemoglu, D., Makhdoumi, A., Malekian, A., Ozdaglar, A.: Testing, voluntary social distancing and the spread of an infection. Technical report, National Bureau of Economic Research (2020)
    1. Acemoglu D, Chernozhukov V, Werning I, Whinston MD. Optimal targeted lockdowns in a multigroup sir model. Am. Econ. Rev. Insights. 2021;3(4):487–502. doi: 10.1257/aeri.20200590. - DOI
    1. Alvarez F, Argente D, Lippi F. A simple planning problem for COVID-19 lock-down, testing, and tracing. Am. Econ. Rev. Insights. 2021;3(3):367–82. doi: 10.1257/aeri.20200201. - DOI
    1. Alvarez, F.E., Argente, D., Lippi, F.: A simple planning problem for COVID-19 lockdown. Technical report, National Bureau of Economic Research (2020)
    1. Ash T, Bento AM, Kaffine D, Rao A, Bento AI. Disease-economy trade-offs under alternative epidemic control strategies. Nat. Commun. 2022;13(1):3319. doi: 10.1038/s41467-022-30642-8. - DOI - PMC - PubMed

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