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Taming the spread of an epidemic by lockdown policies

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  • Federico, Salvatore
  • Ferrari, Giorgio

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 to 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 × percentage of susceptible” is kept after a certain date strictly below the critical level of one, although the reproduction number is let to oscillate above one in the last more relaxed phase of lockdown. Finally, an increase in the fluctuations of the transmission rate is shown to give rise to an earlier beginning of the optimal lockdown policy, which is also diluted over a longer period of time.

Suggested Citation

  • Federico, Salvatore & Ferrari, Giorgio, 2021. "Taming the spread of an epidemic by lockdown policies," Journal of Mathematical Economics, Elsevier, vol. 93(C).
  • Handle: RePEc:eee:mateco:v:93:y:2021:i:c:s0304406820301300
    DOI: 10.1016/j.jmateco.2020.102453
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    References listed on IDEAS

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    1. Christian Gollier, 2020. "Cost–benefit analysis of age‐specific deconfinement strategies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(6), pages 1746-1771, December.
    2. Daron Acemoglu & Victor Chernozhukov & Iván Werning & Michael D. Whinston, 2021. "Optimal Targeted Lockdowns in a Multigroup SIR Model," American Economic Review: Insights, American Economic Association, vol. 3(4), pages 487-502, December.
    3. Fernando E. Alvarez & David Argente & Francesco Lippi, 2020. "A Simple Planning Problem for COVID-19 Lockdown," NBER Working Papers 26981, National Bureau of Economic Research, Inc.
    4. Aspri, Andrea & Beretta, Elena & Gandolfi, Alberto & Wasmer, Etienne, 2021. "Mortality containment vs. Economics Opening: Optimal policies in a SEIARD model," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    5. Alexis Akira Toda, 2020. "Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact," Papers 2003.11221, arXiv.org, revised Mar 2020.
    6. Thomas Kruse & Philipp Strack, 2020. "Optimal Control of an Epidemic through Social Distancing," Cowles Foundation Discussion Papers 2229R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2020.
    7. Miclo, Laurent & Weibull, Jörgen W. & Spiro, Daniel, 2020. "Optimal epidemic suppression under an ICU constraint," TSE Working Papers 20-1111, Toulouse School of Economics (TSE).
    8. Laurent Miclo & Daniel Spiro & Jörgen Weibull, 2020. "Optimal epidemic suppression under an ICU constraint ," Working Papers hal-02563023, HAL.
    9. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
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    Cited by:

    1. Caulkins, J.P. & Grass, D. & Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Kuhn, M. & Prskawetz, A. & Sanchez-Romero, M. & Seidl, A. & Wrzaczek, S., 2023. "The hammer and the jab: Are COVID-19 lockdowns and vaccinations complements or substitutes?," European Journal of Operational Research, Elsevier, vol. 311(1), pages 233-250.
    2. Davide Torre & Simone Marsiglio & Franklin Mendivil & Fabio Privileggi, 2024. "Stochastic disease spreading and containment policies under state-dependent probabilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 127-168, February.
    3. Thomas Hellmann & Veikko Thiele, 2022. "A theory of voluntary testing and self‐isolation in an ongoing pandemic," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 873-911, October.
    4. Raouf Boucekkine & Shankha Chakraborty & Aditya Goenka & Lin Liu, 2024. "A Brief Tour of Economic Epidemiology Modelling," LIDAM Discussion Papers IRES 2024002, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    5. Alessandro Ramponi & Maria Elisabetta Tessitore, 2022. "The economic cost of social distancing during a pandemic: an optimal control approach in the SVIR model," Papers 2208.04908, arXiv.org.
    6. Jacek Rothert, 2021. "Optimal federal transfers during uncoordinated response to a pandemic," GRAPE Working Papers 58, GRAPE Group for Research in Applied Economics.
    7. Fausto Cavalli & Ahmad Naimzada & Daniela Visetti, 2023. "Dynamical analysis of healthcare policy effects in an integrated economic-epidemiological model," Working Papers 521, University of Milano-Bicocca, Department of Economics.
    8. Jacek Rothert, 2022. "Optimal federal transfers during uncoordinated response to a pandemic," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1124-1153, October.
    9. Michael Freiberger & Dieter Grass & Michael Kuhn & Andrea Seidl & Stefan Wrzaczek, 2022. "Chasing up and locking down the virus: Optimal pandemic interventions within a network," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1182-1217, October.
    10. Rabah Amir & Raouf Boucekkine, 2022. "Introduction to the special issue on new insights into economic epidemiology: Theory and policy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 861-872, October.
    11. Alessandro Basurto & Herbert Dawid & Philipp Harting & Jasper Hepp & Dirk Kohlweyer, 2023. "How to design virus containment policies? A joint analysis of economic and epidemic dynamics under the COVID-19 pandemic," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(2), pages 311-370, April.
    12. Gian Paolo Clemente & Rosanna Grassi & Giorgio Rizzini, 2022. "The effect of the pandemic on complex socio-economic systems: community detection induced by communicability," Papers 2201.12618, arXiv.org.
    13. Federico, Salvatore & Ferrari, Giorgio & Torrente, Maria-Laura, 2022. "Optimal Vaccination in a SIRS Epidemic Model," Center for Mathematical Economics Working Papers 667, Center for Mathematical Economics, Bielefeld University.
    14. La Torre, Davide & Marsiglio,Simone & Mendivil,Franklin & Privileggi, Fabio, 2022. "Stochastic Disease Spreading and Containment Policies under State-Dependent Probabilities," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202205, University of Turin.

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