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Taming the Spread of an Epidemic by Lockdown Policies

Salvatore Federico and Giorgio Ferrari
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Salvatore Federico: Center for Mathematical Economics, Bielefeld University
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University

No 639, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We study the problem of a policymaker who aims at taming the spread of an epidemic while minimizing its associated social costs. The main feature of our model lies in the fact that the disease's transmission rate is a diffusive stochastic process whose trend can be adjusted via costly confinement policies. We provide a complete theoretical analysis, as well as numerical experiments illustrating the structure of the optimal lockdown policy. In all our experiments the latter is characterized by three distinct periods: the epidemic is first let freely evolve, then vigorously tamed, and finally a less stringent containment should be adopted. Moreover, the optimal containment policy is such that the product "reproduction number x percentage of susceptible" is kept after a certain date strictly below the critical level of one, although the reproduction number is let oscillate above one in the last more relaxed phase of lockdown.

Keywords: SIR model; optimal stochastic control; viscosity solution; epidemic; lockdown (search for similar items in EconPapers)
Pages: 17
Date: 2020-07-31
New Economics Papers: this item is included in nep-hea and nep-ore
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https://pub.uni-bielefeld.de/download/2945084/2945683 First Version, 2020 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:639

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