Understanding Nash epidemics
Open accessAbstract
Faced with a dangerous epidemic humans will spontaneously social distance to reduce their risk of infection at a socioeconomic cost. Compartmentalized epidemic models have been extended to include this endogenous decision making: Individuals choose their behavior to optimize a utility function, self-consistently giving rise to population behavior. Here, we study the properties of the resulting Nash equilibria, in which no member of the population can gain an advantage by unilaterally adopting different behavior. We leverage an analytic solution that yields fully time-dependent rational population behavior to obtain, 1) a simple relationship between rational social distancing behavior and the current number of infections; 2) scaling results for how the infection peak and number of total cases depend on the cost of contracting the disease; 3) characteristic infection costs that divide regimes of strong and weak behavioral response; 4) a closed form expression for the value of the utility. We discuss how these analytic results provide a deep and intuitive understanding of the disease dynamics, useful for both individuals and policymakers. In particular, the relationship between social distancing and infections represents a heuristic that could be communicated to the population to encourage, or “bootstrap,” rational behavior.
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A cFFL consists of a fast direct pathway and a slow indirect pathway, which filters out short-lived and spurious signals by integrating these inputs.
“A cFFL consists of a fast direct pathway and a slow indirect pathway, which filters out short-lived and spurious signals by integrating these inputs.”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [46]
The Results section discusses Nash-equilibrium social distancing and epidemic dynamics, not coherent feed-forward loops. Searches for “cFFL,” fast and slow pathways, and signal filtering found no passage in our copy addressing the claim. (LLM, conf=0.78)
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Scantamburlo, M., Proverbio, D., & Giordano, G. (2025) · medRxiv · doi:10.1101/2025.11.26.25341041
“Despite recent attempts to include multiple aspects in a single dynamical behavioural-epidemiological model (we recall, e.g., game-theoretic [8, 9] or multi-agent approaches [10, 11], as well as compartmental models integrating individual adherence directly [12, 13] or via frameworks from…”
Impacts of reinforcement learning-driven subsidy policies on evolutionary vaccination dynamics
Hou, Y., Huang, Y., Lu, Y., et al. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0306752
Mathematical Models in Disease Transmission: A Case Study of Measles with an Optimized SIRS Model
Yuan, D. (2026) · International Symposium on Big Data and Applied Statistics (ISBDAS) · doi:10.1109/isbdas69350.2026.11484218
“Early compartmental models focused primarily on understanding epidemic dynamics in naive populations, establishing fundamental concepts such as the basic reproduction number and herd immunity thresholds [6].”
Host behavioral responses to perceived risk shape spatial disease dynamicsPreprint
Clement, D. T., Holt, R. D., Ruktanonchai, N., Saucedo, O., & Kortessis, N. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.05.25.726839
Mallick, P., Müller, L., Marín-Carballo, A. B., et al. (2026) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2026.118649
“It signifies an individual’s exit from the infectious state, a transition driven by the comprehensive behavioral shifts that occur after diagnosis, supported by counseling and other non-pharmaceutical measures [50,51].”
- Authors
- Schnyder, S. K., Molina, J. J., Yamamoto, R., & Turner, M. S.
- Affiliations
- Institute of Industrial Science, The University of Tokyo (JP)
- Kyoto University (JP)
- Department of Chemical Engineering
- University of Warwick (GB)
- Corresponding author
- Schnyder, Simon K.
- Turner, Matthew S.
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2025-02-27
- Volume
- 122
- Issue
- 9
- Pages
- e2409362122-e2409362122
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC11892628
- OpenAlex
- W4408019161
- Semantic Scholar
- 0e8ae1ffba7e2040a89ae99b81aeafb9d3c5e60a
- Cited by
- 12
- References
- 92
- Citations by year
- 2026: 6 · 2025: 6
- FWCI
- 10.99
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Warwick Research Archive Portal (University of Warwick) (acceptedVersion)
- Funders
- Japan Society for the Promotion of Science London (20H00129, 20H05619, 22H04841, 22K14012, 23H04508, JPJSCCA20230002, L19547)
- Leverhulme Trust (IAF-2019-019)
- Topics
- Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
- Physical Sciences › Mathematics › Modeling and Simulation › COVID-19 epidemiological studies
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Keywords
- Nash equilibrium, epidemic dynamics, social distancing, rational choice, compartmental epidemic model, utility maximization, infection peak, analytical solution, epidemic control policy
- MeSH terms
- Physical Distancing, COVID-19, Humans, Epidemics
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