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Peer-reviewedCC BY 4.0Physical Review Research

Emergent dilemma and periodic oscillation in behavioral epidemics with nonlinear feedback

  • Longzhao Liu1
  • Hongwei Zheng2
  • Yajing Hao1
  • Qun Wang3
  • Xin Wang1
  • Shaoting Tang1,4
4 affiliations
  1. 1Beihang University
  2. 2Beijing Academy of Blockchain and Edge Computing
  3. 3Beijing Wuzi University
  4. 4Binzhou Medical University
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Abstract

Human behaviors, particularly nonpharmaceutical interventions (NPIs), are dynamically coupled with epidemic spreading. However, most models assume a linear relationship between perceived risk and infection rates, failing to capture the nonlinear nature of real-world behavioral responses. Here, we propose a behavioral epidemic model by incorporating nonlinear feedback and social influence, and analytically derive its critical thresholds. Notably, once the infection rate exceeds a critical threshold, the fraction of NPI adopters abruptly drops to zero, in contrast to classic findings in linear models. This paradoxical decline indicates a social dilemma: While abandoning NPIs is individually optimal at high infection rates, it collectively triggers an explosive epidemic surge. Furthermore, as the intensity of social influence increases, the system undergoes a Hopf bifurcation leading to periodic oscillations, which reflects a vicious cycle of recurrent epidemic waves. Finally, we confirm the robustness of this NPI-abandonment dilemma in networked populations. Our work illustrates rich emergent dynamics, challenging traditional perspectives on behavioral epidemiology.

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Cite

BibTeXRIS
BibTeX
@article{liu2026emergent,
  title = {{Emergent dilemma and periodic oscillation in behavioral epidemics with nonlinear feedback}},
  author = {Longzhao Liu and Hongwei Zheng and Yajing Hao and Qun Wang and Xin Wang and Shaoting Tang},
  journal = {Physical Review Research},
  year = {2026},
  month = oct,
  doi = {10.1103/zrk4-g7fj},
  url = {https://link.aps.org/doi/10.1103/zrk4-g7fj},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Emergent dilemma and periodic oscillation in behavioral epidemics with nonlinear feedback
AU  - Longzhao Liu
AU  - Hongwei Zheng
AU  - Yajing Hao
AU  - Qun Wang
AU  - Xin Wang
AU  - Shaoting Tang
PY  - 2026
DA  - 2026/10/14
JO  - Physical Review Research
DO  - 10.1103/zrk4-g7fj
UR  - https://link.aps.org/doi/10.1103/zrk4-g7fj
AB  - Human behaviors, particularly nonpharmaceutical interventions (NPIs), are dynamically coupled with epidemic spreading. However, most models assume a linear relationship between perceived risk and infection rates, failing to capture the nonlinear nature of real-world behavioral responses. Here, we propose a behavioral epidemic model by incorporating nonlinear feedback and social influence, and analytically derive its critical thresholds. Notably, once the infection rate exceeds a critical threshold, the fraction of NPI adopters abruptly drops to zero, in contrast to classic findings in linear models. This paradoxical decline indicates a social dilemma: While abandoning NPIs is individually optimal at high infection rates, it collectively triggers an explosive epidemic surge. Furthermore, as the intensity of social influence increases, the system undergoes a Hopf bifurcation leading to periodic oscillations, which reflects a vicious cycle of recurrent epidemic waves. Finally, we confirm the robustness of this NPI-abandonment dilemma in networked populations. Our work illustrates rich emergent dynamics, challenging traditional perspectives on behavioral epidemiology.
SN  - 2643-1564
ER  -