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Infectious diseases and social distancing under state-dependent probabilities

Author

Listed:
  • Davide La Torre

    (SKEMA Business School and Université Côte d’Azur)

  • Simone Marsiglio

    (University of Pisa)

  • Fabio Privileggi

    (University of Turin)

Abstract

We analyze the implications of infectious diseases and social distancing in an extended SIS framework to allow for the presence of stochastic shocks with state dependent probabilities. Random shocks give rise to the diffusion of a new strain of the disease which affects both the number of infectives and the average biological characteristics of the pathogen causing the disease. The probability of such shock realizations changes with the level of disease prevalence and we analyze how the properties of the state-dependent probability function affect the long run epidemiological outcome which is characterized by an invariant probability distribution supported on a range of positive prevalence levels. We show that social distancing reduces the size of the support of the steady state distribution decreasing thus the variability of disease prevalence, but in so doing it also shifts the support rightward allowing eventually for more infectives than in an uncontrolled framework. Nevertheless, social distancing is an effective control measure since it concentrates most of the mass of the distribution toward the lower extreme of its support.

Suggested Citation

  • Davide La Torre & Simone Marsiglio & Fabio Privileggi, 2024. "Infectious diseases and social distancing under state-dependent probabilities," Annals of Operations Research, Springer, vol. 337(3), pages 993-1008, June.
    • Handle: RePEc:spr:annopr:v:337:y:2024:i:3:d:10.1007_s10479-023-05409-z
    DOI: 10.1007/s10479-023-05409-z
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    References listed on IDEAS

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    1. Luca Gori & Piero Manfredi & Simone Marsiglio & Mauro Sodini, 2022. "COVID‐19 epidemic and mitigation policies: Positive and normative analyses in a neoclassical growth model," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 968-992, October.
    2. La Torre, Davide & Malik, Tufail & Marsiglio, Simone, 2020. "Optimal control of prevention and treatment in a basic macroeconomic–epidemiological model," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 100-108.
    3. Chakraborty, Shankha & Papageorgiou, Chris & Pérez Sebastián, Fidel, 2010. "Diseases, infection dynamics, and development," Journal of Monetary Economics, Elsevier, vol. 57(7), pages 859-872, October.
    4. Martin S Eichenbaum & Sergio Rebelo & Mathias Trabandt, 2021. "The Macroeconomics of Epidemics [Economic activity and the spread of viral diseases: Evidence from high frequency data]," The Review of Financial Studies, Society for Financial Studies, vol. 34(11), pages 5149-5187.
    5. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2014. "Infectious diseases and economic growth," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 34-53.
    6. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-similar measures in multi-sector endogenous growth models," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 40-56.
    7. Mark Gersovitz & Jeffrey S. Hammer, 2004. "The Economical Control of Infectious Diseases," Economic Journal, Royal Economic Society, vol. 114(492), pages 1-27, January.
    8. Harrison Hong & Neng Wang & Jinqiang Yang, 2021. "Implications of Stochastic Transmission Rates for Managing Pandemic Risks [Comparison of deterministic and stochastic SIS and SIR models in discrete time]," The Review of Financial Studies, Society for Financial Studies, vol. 34(11), pages 5224-5265.
    9. L. Montrucchio & F. Privileggi, 1999. "Fractal steady states instochastic optimal control models," Annals of Operations Research, Springer, vol. 88(0), pages 183-197, January.
    10. Torre, Davide La & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2019. "A stochastic economic growth model with health capital and state-dependent probabilities," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 81-93.
    11. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Epidemics and macroeconomic outcomes: Social distancing intensity and duration," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    12. Mitra, Tapan & Privileggi, Fabio, 2009. "On Lipschitz continuity of the iterated function system in a stochastic optimal growth model," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 185-198, January.
    13. Federico, Salvatore & Ferrari, Giorgio, 2021. "Taming the spread of an epidemic by lockdown policies," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    14. Tapan Mitra & Luigi Montrucchio & Fabio Privileggi, 2003. "The nature of the steady state in models of optimal growth under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 39-71, December.
    15. Aditya Goenka & Lin Liu, 2012. "Infectious diseases and endogenous fluctuations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 125-149, May.
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    More about this item

    Keywords

    Economic epidemiology; Social distancing; State-dependent probability;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • H50 - Public Economics - - National Government Expenditures and Related Policies - - - General
    • I10 - Health, Education, and Welfare - - Health - - - General

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