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A stochastic model for the influence of social distancing on loneliness

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  • Fontanari, José F.

Abstract

The short-term economic consequences of the critical measures employed to curb the transmission of Covid-19 are all too familiar, but the consequences of isolation and loneliness resulting from those measures on the mental well-being of the population and their ensuing long-term economic effects are largely unknown. Here we offer a stochastic agent-based model to investigate social restriction measures in a community where the feelings of loneliness of the agents dwindle when they are socializing and grow when they are alone. In addition, the intensity of those feelings, which are measured by a real variable that we term degree of loneliness, determines whether the agent will seek social contact or not. We find that decrease of the number, quality or duration of social contacts lead the community to enter a regime of burnout in which the degree of loneliness diverges, although the number of lonely agents at a given moment amounts to only a fraction of the total population. This regime of mental breakdown is separated from the healthy regime, where the degree of loneliness is finite, by a continuous phase transition. We show that the community dynamics is described extremely well by a simple mean-field theory so our conclusions can be easily verified for different scenarios and parameter settings. The appearance of the burnout regime illustrates neatly the side effects of social distancing, which give to many of us the choice between physical infection and mental breakdown.

Suggested Citation

  • Fontanari, José F., 2021. "A stochastic model for the influence of social distancing on loneliness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
  • Handle: RePEc:eee:phsmap:v:584:y:2021:i:c:s0378437121006403
    DOI: 10.1016/j.physa.2021.126367
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    References listed on IDEAS

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    1. Nicola Bellomo & Richard Bingham & Mark A.J. Chaplain & Giovanni Dosi & Guido Forni & Damian A. Knopoff & John Lowengrub & Reidun Twarock & Maria Enrica Virgillito, 2020. "A multi-scale model of virus pandemic: Heterogeneous interactive entities in a globally connected world," LEM Papers Series 2020/16, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    2. Andrew J. Oswald & Eugenio Proto & Daniel Sgroi, 2015. "Happiness and Productivity," Journal of Labor Economics, University of Chicago Press, vol. 33(4), pages 789-822.
    3. Peter Hardy & Leandro Soriano Marcolino & José F. Fontanari, 2021. "The paradox of productivity during quarantine: an agent-based simulation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-6, January.
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    Cited by:

    1. Alexandru Topîrceanu, 2024. "A Spatial Agent-Based Model for Studying the Effect of Human Mobility Patterns on Epidemic Outbreaks in Urban Areas," Mathematics, MDPI, vol. 12(17), pages 1-20, September.
    2. José F. Fontanari, 2023. "Stochastic Simulations of Casual Groups," Mathematics, MDPI, vol. 11(9), pages 1-16, May.

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