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Covid and social distancing with a heterogenous population

Economic Theory (2021)Cite this article

Abstract

Motivated by the Covid-19 epidemic, we build a SIR model with private decisions on social distancing and population heterogeneity in terms of infection-induced fatality rates, and calibrate it to UK data to understand the quantitative importance of these assumptions. Compared to our model, the calibrated benchmark version with constant mean contact rate significantly over-predicts the mean contact rate, the death toll, herd immunity and prevalence peak. Instead, the calibrated counterfactual version with endogenous social distancing but no heterogeneity massively under-predicts these statistics. We use our calibrated model to understand how the impact of mitigating policies on the epidemic may depend on the responses these policies induce across the various population segments. We find that policies that shut down some of the essential sectors have a stronger impact on the death toll than on infections and herd immunity compared to policies that shut down non-essential sectors. Furthermore, there might not be an after-wave after policies that shut down some of the essential sectors are lifted. Restrictions on social distancing can generate welfare gains relative to the case of no intervention. Milder but longer restrictions on less essential activities might be better in terms of these welfare gains than stricter but shorter restrictions, whereas the opposite might be the case for restrictions on more essential activities. Finally, shutting down some of the more essential sectors might generate larger welfare gains than shutting down the less essential sectors.

References

  • Acemoglou, D., Chernozhukov, N., Werning, I., Winston, M.D.: A multi-risk SIR model with optimally targeted lockdown. CEMMAP Working Paper CWP14/20 (2020)

  • Alvarez, F., Argente, D., Lippi, F.: A simple planning problem for COVID-19 lockdown, testing and tracing. Am. Econ. Rev. Insights (2020)

  • Anderson, R.M., Anderson, B., May, R.M.: Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford (1992)

    Google Scholar 

  • Bodenstein, M., Corsetti, C., Guerrieri, L.: Social distancing and supply disruption in a pandemic. Mimeo (2020)

  • Eichenbaum, M., Rebelo, S., Trabandt, M.: The macroeconomics of epidemics. Mimeo (2020)

  • Farboodi, M., Jarosch, G., Shimer, R.: Internal and External Effects of Social Distancing in a Pandemic. Becker Friedman Institute, Working Paper No 2020-47 (2020)

  • Fenichel, E.P.: Economic considerations for social distancing and behavioral based policies during an epidemic. J. Health Econ. 32, 440–451 (2013). https://doi.org/10.1016/j.jhealeco.2013.01.002

    Article  Google Scholar 

  • Galanis, S.: Social proximity as a tool to fight pandemics. Mimeo (2020)

  • Geoffard, P.-Y., Philipson, T.: Rational epidemics and their public control. Int. Econ. Rev. 37, 603–624 (1996). https://doi.org/10.2307/2527443

    Article  Google Scholar 

  • Glover, A., Heathcote, J., Krueger, D., Rios-Rull, J.V.: Health versus wealth: on the distributional effects of controlling a pandemic. Mimeo (2020)

  • Hall, R.E., Jones, C.I., Klenow, P.J.: Trading off consumption and COVID-19 deaths. Mimeo (2020)

  • Kaplan, G., Moll, B., Violante, G.: Pandemics according to HANK. Mimeo (2020)

  • Keppo, J., Kudlyak, M., Quercioli, E., Smith, L., Wilson, A.: The behavioral SIR model, with applications to the Swine Flu and COVID-19 pandemics. Mimeo (2020)

  • Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. A 115(772), 700–721 (1927). https://doi.org/10.1098/rspa.1927.0118

    Article  Google Scholar 

  • Kniesner, T., Viscusi, K.: The Value of a Statistical Life. Oxford Research Encyclopedia of Economics and Finance (2020). https://doi.org/10.1093/acrefore/9780190625979.013.138

  • Krueger, D., Uhlig, H., Xie, T.: Macroeconomic dynamics and reallocation in an epidemic. Mimeo (2020)

  • Kucharski, A.J., Russell, T.W., Diamond, C., Liu, Y., Edmunds, J., Funk, S., Eggo, R.M.: Early dynamics of transmission and control of COVID-19: a mathematical modelling study. Lancet Infect Dis. (2020). https://doi.org/10.1016/S1473-3099(20)30144-4

    Article  Google Scholar 

  • Linton, N.M., Kobayashi, T., Yang, Y., Hayashi, K., Akhmetzhanov, A.R., Jung, S.-M., Yuan, B., Kinoshita, R., Nishiura, H.: Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data. J. Clin. Med. (2020). https://doi.org/10.3390/jcm9020538

  • Lourenço, J., Paton, R., Ghafari, M., Kraemer, M., Thompson, C., Simmonds, P., Klenerman, P., Gupta, S.: Fundamental principles of epidemic spread highlight the immediate need for large-scale serological surveys to assess the stage of the SARS-CoV-2 epidemic. medRxiv (2020)

  • Maloney, W.F., Taskin, T.: Social distancing and economic activity during COVID-19: a global view. COVID Econ. 13, 157–177 (2020)

    Google Scholar 

  • Reluga, T.C.: Game theory of social distancing in response to an epidemic. PLoS Comput. Biol. 6(5), e1000793 (2010). https://doi.org/10.1371/journal.pcbi.1000793

    Article  Google Scholar 

  • Rowthorn, R., Toxvaerd, F.: The optimal control of infectious diseases via prevention and treatment. Mimeo (2017)

  • Toxvaerd, F.: Rational disinhibition and externalities in prevention. Int. Econ. Rev. 60(4), 1737–1755 (2019). https://doi.org/10.1111/iere.12402

    Article  Google Scholar 

  • Toxvaerd, F.: Equilibrium Social Distancing. Cambridge-INET Working Paper Series No: 2020/08 (2020)

  • Wu, D., Wu, T., Liu, Q., Yang, Z.: The SARS-CoV-2 outbreak: what we know. Int. J. Infect. Dis. 94, 44–48 (2020). https://doi.org/10.1016/j.ijid.2020.03.004

    Article  Google Scholar 

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  1. University of Kent, Canterbury, UK

    Miltiadis Makris

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  1. Miltiadis Makris
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Correspondence to Miltiadis Makris.

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Makris, M. Covid and social distancing with a heterogenous population. Econ Theory (2021). https://doi.org/10.1007/s00199-021-01377-2

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  • DOI: https://doi.org/10.1007/s00199-021-01377-2

Keywords

  • COVID-19
  • Epidemiology
  • SIR model
  • Social distancing
  • Equilibrium
  • Lockdowns

JEL Classification

  • C61
  • C72
  • C73
  • H41
  • I12
  • I18