IDEAS home Printed from https://ideas.repec.org/a/plo/pcbi00/1000793.html
   My bibliography  Save this article

Game Theory of Social Distancing in Response to an Epidemic

Author

Listed:
  • Timothy C Reluga

Abstract

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
    as

    Download full text from publisher

    File URL: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1000793
    Download Restriction: no

    File URL: https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1000793&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pcbi.1000793?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Neil M. Ferguson & Derek A.T. Cummings & Simon Cauchemez & Christophe Fraser & Steven Riley & Aronrag Meeyai & Sopon Iamsirithaworn & Donald S. Burke, 2005. "Strategies for containing an emerging influenza pandemic in Southeast Asia," Nature, Nature, vol. 437(7056), pages 209-214, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tamer Edirne & Dilek Avci & Burçak Dagkara & Muslum Aslan, 2011. "Knowledge and anticipated attitudes of the community about bird flu outbreak in Turkey, 2007–2008: a survey-based descriptive study," International Journal of Public Health, Springer;Swiss School of Public Health (SSPH+), vol. 56(2), pages 163-168, April.
    2. Wei Zhong, 2017. "Simulating influenza pandemic dynamics with public risk communication and individual responsive behavior," Computational and Mathematical Organization Theory, Springer, vol. 23(4), pages 475-495, December.
    3. Linus Nyiwul, 2021. "Epidemic Control and Resource Allocation: Approaches and Implications for the Management of COVID-19," Studies in Microeconomics, , vol. 9(2), pages 283-305, December.
    4. Zhongqiang Bai & Juanle Wang & Mingming Wang & Mengxu Gao & Jiulin Sun, 2018. "Accuracy Assessment of Multi-Source Gridded Population Distribution Datasets in China," Sustainability, MDPI, vol. 10(5), pages 1-15, April.
    5. Andrew J Black & Joshua V Ross, 2013. "Estimating a Markovian Epidemic Model Using Household Serial Interval Data from the Early Phase of an Epidemic," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-8, August.
    6. Li, Qian & Xiao, Yanni, 2023. "Analysis of a hybrid SIR model combining the fixed-moments pulse interventions with susceptibles-triggered threshold policy," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    7. Nguyen, Le Khanh Ngan & Howick, Susan & Megiddo, Itamar, 2024. "A framework for conceptualising hybrid system dynamics and agent-based simulation models," European Journal of Operational Research, Elsevier, vol. 315(3), pages 1153-1166.
    8. Edoardo Di Porto & Paolo Naticchioni & Vincenzo Scrutinio, 2020. "Partial Lockdown and the Spread of Covid-19: Lessons from the Italian Case," CSEF Working Papers 569, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    9. Khan, Mohsin & Abdalgader, Tarteel & Pedersen, Michael & Zhang, Lai, 2025. "Interactive effects of climate change and human mobility on dengue transmission," Ecological Modelling, Elsevier, vol. 499(C).
    10. Eva K. Lee & Ferdinand Pietz & Bernard Benecke & Jacquelyn Mason & Greg Burel, 2013. "Advancing Public Health and Medical Preparedness with Operations Research," Interfaces, INFORMS, vol. 43(1), pages 79-98, February.
    11. Sabina Alistar & Elisa Long & Margaret Brandeau & Eduard Beck, 2014. "HIV epidemic control—a model for optimal allocation of prevention and treatment resources," Health Care Management Science, Springer, vol. 17(2), pages 162-181, June.
    12. Huberts, Nick F.D. & Thijssen, Jacco J.J., 2023. "Optimal timing of non-pharmaceutical interventions during an epidemic," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1366-1389.
    13. Bekiros, Stelios & Kouloumpou, Dimitra, 2020. "SBDiEM: A new mathematical model of infectious disease dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    14. Akira Watanabe & Hiroyuki Matsuda, 2023. "Effectiveness of feedback control and the trade-off between death by COVID-19 and costs of countermeasures," Health Care Management Science, Springer, vol. 26(1), pages 46-61, March.
    15. Andy Hong & Sandip Chakrabarti, 2023. "Compact living or policy inaction? Effects of urban density and lockdown on the COVID-19 outbreak in the US," Urban Studies, Urban Studies Journal Limited, vol. 60(9), pages 1588-1609, July.
    16. Lawrence M. Wein & Michael P. Atkinson, 2009. "Assessing Infection Control Measures for Pandemic Influenza," Risk Analysis, John Wiley & Sons, vol. 29(7), pages 949-962, July.
    17. Savachkin, Alex & Uribe, Andrés, 2012. "Dynamic redistribution of mitigation resources during influenza pandemics," Socio-Economic Planning Sciences, Elsevier, vol. 46(1), pages 33-45.
    18. Guihua Wang, 2022. "Stay at home to stay safe: Effectiveness of stay‐at‐home orders in containing the COVID‐19 pandemic," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2289-2305, May.
    19. Leach, Melissa & MacGregor, Hayley & Scoones, Ian & Wilkinson, Annie, 2021. "Post-pandemic transformations: How and why COVID-19 requires us to rethink development," World Development, Elsevier, vol. 138(C).
    20. Amy Wesolowski & Caroline O Buckee & Deepa K Pindolia & Nathan Eagle & David L Smith & Andres J Garcia & Andrew J Tatem, 2013. "The Use of Census Migration Data to Approximate Human Movement Patterns across Temporal Scales," PLOS ONE, Public Library of Science, vol. 8(1), pages 1-8, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pcbi00:1000793. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ploscompbiol (email available below). General contact details of provider: https://journals.plos.org/ploscompbiol/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.