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Understanding Nash epidemics.

Simon K Schnyder1, John J Molina2, Ryoichi Yamamoto2

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Summary
This summary is machine-generated.

Individuals rationally reduce social contact during epidemics to minimize infection risk. This study models this behavior, revealing key dynamics between social distancing and infection spread for public health insights.

Keywords:
control theoryepidemiologygame theorymathematical modelingmean-field games

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Area of Science:

  • Epidemiology
  • Behavioral Economics
  • Mathematical Modeling

Background:

  • Epidemics prompt social distancing to mitigate infection risk, incurring socioeconomic costs.
  • Traditional epidemic models often overlook endogenous individual decision-making.
  • Integrating rational choice into epidemic models is crucial for understanding population behavior.

Purpose of the Study:

  • To analyze Nash equilibria in epidemic models with endogenous social distancing.
  • To derive time-dependent rational population behavior using an analytic solution.
  • To understand the relationship between individual behavior and population-level disease dynamics.

Main Methods:

  • Utilizing an analytic solution for compartmentalized epidemic models.
  • Incorporating individual utility optimization for behavior determination.
  • Analyzing Nash equilibria to find stable population behaviors.

Main Results:

  • A direct relationship between rational social distancing and current infection levels was established.
  • Scaling laws were derived for infection peaks and total cases based on disease cost.
  • Characteristic infection costs defining behavioral response regimes were identified.
  • A closed-form expression for the utility value was obtained.

Conclusions:

  • Analytic results offer intuitive insights into epidemic dynamics for individuals and policymakers.
  • The social distancing-infection relationship can serve as a heuristic to promote rational behavior.
  • Understanding rational behavior is key to effective public health interventions during epidemics.