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Mathematical Biosciences and Engineering

2026, Volume 23, Issue 1: 148-171. doi: 10.3934/mbe.2026007
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Self-organized social distancing during epidemics when the force of infection depends on susceptible and infectious behavior

  • 1.
    Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
  • 2.
    Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan
  • 3.
    Department of Mathematics and Physical Sciences, La Trobe University, Bundoora, VIC 3086, Australia
  • 4.
    Australian Centre for Artificial Intelligence in Medical Innovation, La Trobe University, Bundoora, VIC 3086, Australia
  • 5.
    Universal Biology Institute, The University of Tokyo, Tokyo 113-0033, Japan
  • 6.
    Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
  • 7.
    Department of Physics, University of Warwick, Coventry CV4 7AL, UK
  • 8.
    Institute for Global Pandemic Planning, University of Warwick, Coventry CV4 7AL, UK
  • Published: 02 December 2025

  • During epidemics, individuals may adjust their social behavior in response to the threat. This may affect the course of the epidemic, and, in turn, again modify people's behavior. Game theoretically, the system may end up in a Nash equilibrium, where no member of the population can benefit by unilaterally changing their behavior. Compartmentalized epidemic models can incorporate such endogenous decision making, where individuals try to optimize a utility function via their behavior. Typically, such models can only be solved numerically. Here, we extend a recently discovered analytic solution for time-dependent social distancing and the corresponding epidemic dynamics: now, the probability of an infection taking place can depend on both the susceptible and infectious individual behaviors. We show that the more effectively the susceptible individual can reduce the probability of infection, the more self-organized social distancing is expected to occur. The previously identified heuristic that the strength of rational social distancing is proportional to both the perceived infection cost and prevalence is found to also hold in the generalized model.

    Citation: Simon K. Schnyder, John J. Molina, Joel C. Miller, Ryoichi Yamamoto, Tetsuya J. Kobayashi, Matthew S. Turner. Self-organized social distancing during epidemics when the force of infection depends on susceptible and infectious behavior[J]. Mathematical Biosciences and Engineering, 2026, 23(1): 148-171. doi: 10.3934/mbe.2026007

    Related Papers:

  • During epidemics, individuals may adjust their social behavior in response to the threat. This may affect the course of the epidemic, and, in turn, again modify people's behavior. Game theoretically, the system may end up in a Nash equilibrium, where no member of the population can benefit by unilaterally changing their behavior. Compartmentalized epidemic models can incorporate such endogenous decision making, where individuals try to optimize a utility function via their behavior. Typically, such models can only be solved numerically. Here, we extend a recently discovered analytic solution for time-dependent social distancing and the corresponding epidemic dynamics: now, the probability of an infection taking place can depend on both the susceptible and infectious individual behaviors. We show that the more effectively the susceptible individual can reduce the probability of infection, the more self-organized social distancing is expected to occur. The previously identified heuristic that the strength of rational social distancing is proportional to both the perceived infection cost and prevalence is found to also hold in the generalized model.



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