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On the management of population immunity

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  • Toxvaerd, Flavio
  • Rowthorn, Robert

Abstract

This paper considers a susceptible-infected-recovered type model of infectious diseases, such as COVID-19 or swine flu, in which costly treatment or vaccination confers immunity on recovered individuals. Once immune, individuals indirectly protect the remaining susceptibles, who benefit from a measure of herd immunity. Treatment and vaccination directly induce such herd immunity, which builds up over time. Optimal treatment is shown to involve intervention at early stages of the epidemic, while optimal vaccination may defer intervention to intermediate stages. Thus, while treatment and vaccination have superficial similarities, their effects and desirability at different stages of the epidemic are different. Equilibrium vaccination is qualitatively similar to socially optimal vaccination, while equilibrium treatment differs in nature from socially optimal treatment. The optimal policies are compared to traditional non-economic public health interventions which rely on herd immunity thresholds.

Suggested Citation

  • Toxvaerd, Flavio & Rowthorn, Robert, 2022. "On the management of population immunity," Journal of Economic Theory, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:jetheo:v:204:y:2022:i:c:s0022053122000916
    DOI: 10.1016/j.jet.2022.105501
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    Cited by:

    1. Bizzarri, Matteo & Panebianco, Fabrizio & Pin, Paolo, 2025. "Homophily and infections: Static and dynamic effects," Games and Economic Behavior, Elsevier, vol. 150(C), pages 235-259.
    2. Makris, M. & Toxvaerd, F., 2020. "Great Expectations: Social Distancing in Anticipation of Pharmaceutical Innovations," Cambridge Working Papers in Economics 2097, Faculty of Economics, University of Cambridge.
    3. Acurio Vásconez, Verónica & Damette, Olivier & Shanafelt, David W., 2023. "Macroepidemics and unconventional monetary policy," Economic Modelling, Elsevier, vol. 126(C).
    4. Simon K Schnyder & John J Molina & Ryoichi Yamamoto & Matthew S Turner, 2023. "Rational social distancing in epidemics with uncertain vaccination timing," PLOS ONE, Public Library of Science, vol. 18(7), pages 1-19, July.
    5. Charles Shaw & Silvio Vanadia, 2022. "Utilitarianism on the front lines: COVID-19, public ethics, and the "hidden assumption" problem," Papers 2205.01957, arXiv.org.
    6. 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.
    7. Carnehl, Christoph & Fukuda, Satoshi & Kos, Nenad, 2023. "Epidemics with behavior," Journal of Economic Theory, Elsevier, vol. 207(C).
    8. Carmen Camacho & Chrysovalantis Vasilakis, 2023. "Antivax and inequality," Working Papers hal-03693126, HAL.
    9. Toxvaerd, F.M.O, 2020. "Equilibrium Social Distancing," Cambridge Working Papers in Economics 2021, Faculty of Economics, University of Cambridge.
    10. Auld, M. Christopher & Toxvaerd, Flavio, 2021. "The Great Covid-19 Vaccine Rollout: Behavioural And Policy Responses," National Institute Economic Review, National Institute of Economic and Social Research, vol. 257, pages 14-35, August.
    11. Joshua S. Gans, 2023. "Vaccine Hesitancy, Passports, And The Demand For Vaccination," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(2), pages 641-652, May.
    12. Carmen Camacho & Chrysovalantis Vasilakis, 2024. "Transmissible diseases, vaccination, and inequality," PSE-Ecole d'économie de Paris (Postprint) halshs-04805658, HAL.
    13. Marco Tolotti & Jorge Yepez, 2026. "Uncertainty in vaccination behavior: Social norms, network effects, and policy challenges," Journal of Evolutionary Economics, Springer, vol. 36(2), pages 1-39, August.
    14. Ze Chen & Bingzheng Chen & Yu Mao, 2024. "Fence off Black Swans: The Economics of Insurance for Vaccine Injury," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(5), pages 995-1025, October.
    15. Christopher Avery, 2021. "A Simple Model of Social Distancing and Vaccination," NBER Working Papers 29463, National Bureau of Economic Research, Inc.
    16. Simon K Schnyder & John J Molina & Ryoichi Yamamoto & Matthew S Turner, 2023. "Rational social distancing policy during epidemics with limited healthcare capacity," PLOS Computational Biology, Public Library of Science, vol. 19(10), pages 1-24, October.
    17. Carmen Camacho & Chrysovalantis Vasilakis, 2024. "Transmissible diseases, vaccination, and inequality," Post-Print halshs-04805658, HAL.
    18. Camacho, Carmen & Vasilakis, Chrysovalantis, 2023. "Transmissible Diseases, Vaccination and Inequality," IZA Discussion Papers 16504, IZA Network @ LISER.
    19. Fezzi, Carlo & Fanghella, Valeria, 2021. "Tracking GDP in real-time using electricity market data: Insights from the first wave of COVID-19 across Europe," European Economic Review, Elsevier, vol. 139(C).
    20. Nikhil Vellodi & Joshua Weiss, 2021. "Optimal Vaccine Policies: Spillovers and Incentives," Working Paper 21-06, Federal Reserve Bank of Richmond.

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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health

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