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Game Theory of Social Distancing in Response to an Epidemic


  • Timothy C Reluga


Social distancing practices are changes in behavior that prevent disease transmission by reducing contact rates between susceptible individuals and infected individuals who may transmit the disease. Social distancing practices can reduce the severity of an epidemic, but the benefits of social distancing depend on the extent to which it is used by individuals. Individuals are sometimes reluctant to pay the costs inherent in social distancing, and this can limit its effectiveness as a control measure. This paper formulates a differential-game to identify how individuals would best use social distancing and related self-protective behaviors during an epidemic. The epidemic is described by a simple, well-mixed ordinary differential equation model. We use the differential game to study potential value of social distancing as a mitigation measure by calculating the equilibrium behaviors under a variety of cost-functions. Numerical methods are used to calculate the total costs of an epidemic under equilibrium behaviors as a function of the time to mass vaccination, following epidemic identification. The key parameters in the analysis are the basic reproduction number and the baseline efficiency of social distancing. The results show that social distancing is most beneficial to individuals for basic reproduction numbers around 2. In the absence of vaccination or other intervention measures, optimal social distancing never recovers more than 30% of the cost of infection. We also show how the window of opportunity for vaccine development lengthens as the efficiency of social distancing and detection improve.Author Summary: One of the easiest ways for people to lower their risk of infection during an epidemic is for them to reduce their rate of contact with infectious individuals. However, the value of such actions depends on how the epidemic progresses. Few analyses of behavior change to date have accounted for how changes in behavior change the epidemic wave. In this paper, I calculate the tradeoff between daily social distancing behavior and reductions in infection risk now and in the future. The subsequent analysis shows that, for the parameters and functional forms studied, social distancing is most useful for moderately transmissible diseases. Social distancing is particularly useful when it is inexpensive and can delay the epidemic until a vaccine becomes widely available. However, the benefits of social distancing are small for highly transmissible diseases when no vaccine is available.

Suggested Citation

  • Timothy C Reluga, 2010. "Game Theory of Social Distancing in Response to an Epidemic," PLOS Computational Biology, Public Library of Science, vol. 6(5), pages 1-9, May.
  • Handle: RePEc:plo:pcbi00:1000793
    DOI: 10.1371/journal.pcbi.1000793

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    References listed on IDEAS

    1. Joshua M Epstein & Jon Parker & Derek Cummings & Ross A Hammond, 2008. "Coupled Contagion Dynamics of Fear and Disease: Mathematical and Computational Explorations," PLOS ONE, Public Library of Science, vol. 3(12), pages 1-11, December.
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    As found on the RePEc Biblio, the curated bibliography for Economics:
    1. > Economics of Welfare > Health Economics > Economics of Pandemics > Policy responses > Behavioral


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    Cited by:

    1. Clouston, Sean A.P. & Natale, Ginny & Link, Bruce G., 2021. "Socioeconomic inequalities in the spread of coronavirus-19 in the United States: A examination of the emergence of social inequalities," Social Science & Medicine, Elsevier, vol. 268(C).
    2. Miltiadis Makris, 2020. "Covid and Social Distancing with a Heterogenous Population," Studies in Economics 2002, School of Economics, University of Kent.
    3. Toxvaerd, F.M.O, 2020. "Equilibrium Social Distancing," Cambridge Working Papers in Economics 2021, Faculty of Economics, University of Cambridge.
    4. Amaral, Marco A. & Oliveira, Marcelo M. de & Javarone, Marco A., 2021. "An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Rowthorn, Robert & Toxvaerd, Flavio, 2012. "The Optimal Control of Infectious Diseases via Prevention and Treatment," CEPR Discussion Papers 8925, C.E.P.R. Discussion Papers.
    6. Stephan Leitner, 2021. "On the dynamics emerging from pandemics and infodemics," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 20(1), pages 135-141, June.
    7. Mohler, George & Bertozzi, Andrea L. & Carter, Jeremy & Short, Martin B. & Sledge, Daniel & Tita, George E. & Uchida, Craig D. & Brantingham, P. Jeffrey, 2020. "Impact of social distancing during COVID-19 pandemic on crime in Los Angeles and Indianapolis," Journal of Criminal Justice, Elsevier, vol. 68(C).
    8. Joshua S. Gans, 2020. "The Economic Consequences of R̂ = 1: Towards a Workable Behavioural Epidemiological Model of Pandemics," NBER Working Papers 27632, National Bureau of Economic Research, Inc.
    9. Anna Mummert & Howard Weiss, 2013. "Get the News Out Loudly and Quickly: The Influence of the Media on Limiting Emerging Infectious Disease Outbreaks," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-7, August.
    10. Balazs Pejo & Gergely Biczok, 2020. "Corona Games: Masks, Social Distancing and Mechanism Design," Papers 2006.06674,, revised Oct 2020.
    11. Christopher Avery & William Bossert & Adam Clark & Glenn Ellison & Sara Fisher Ellison, 2020. "An Economist's Guide to Epidemiology Models of Infectious Disease," Journal of Economic Perspectives, American Economic Association, vol. 34(4), pages 79-104, Fall.
    12. Baril-Tremblay, Dominique & Marlats, Chantal & Ménager, Lucie, 2021. "Self-isolation," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    13. Wisarut Suwanprasert, 2020. "COVID-19 and Endogenous Public Avoidance: Insights from an Economic Model," PIER Discussion Papers 128, Puey Ungphakorn Institute for Economic Research, revised Mar 2020.
    14. Han, Dun & Sun, Mei, 2016. "An evolutionary vaccination game in the modified activity driven network by considering the closeness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 49-57.
    15. Ricardo Lagos, 2020. "On Socializing and Social Distancing in Markets: Implications for Retail Prices, Store-level Consumer Density, and Disease Transmission," NBER Working Papers 27724, National Bureau of Economic Research, Inc.
    16. Arazi, R. & Feigel, A., 2021. "Discontinuous transitions of social distancing in the SIR model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    17. Thomas Phelan & Alexis Akira Toda, 2021. "Optimal Epidemic Control in Equilibrium with Imperfect Testing and Enforcement," Papers 2104.04455,
    18. Fabrizio Adriani, 2020. "Social distance, speed of containment, and crowding in/out in a network model of contagion," Discussion Papers 2020-10, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.

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