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Emergent dilemma and periodic oscillation in behavioral epidemics with nonlinear feedback

Longzhao Liu1,2,3,4, Hongwei Zheng5, Yajing Hao6, Qun Wang7,*, Xin Wang1,2,3,4,†, and Shaoting Tang1,2,3,4,8,9,‡

  • 1Institute of Artificial Intelligence, Beihang University, Beijing 100191, China
  • 2Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Beihang University, Beijing 100191, China
  • 3Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing 100191, China
  • 4State Key Laboratory of Complex & Critical Software Environment, Beihang University, Beijing 100191, China
  • 5Beijing Academy of Blockchain and Edge Computing, Beijing 100085, China
  • 6School of Mathematical Sciences, Beihang University, Beijing 100191, China
  • 7School of Logistics, Beijing Wuzi University, Beijing 101149, China
  • 8Hangzhou International Innovation Institute, Beihang University, Hangzhou 311115, China
  • 9Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai 264003, China

  • *Contact author: qunwang@buaa.edu.cn
  • †Contact author: wangxin_1993@buaa.edu.cn
  • ‡Contact author: tangshaoting@buaa.edu.cn
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Phys. Rev. Research 8, 043048 – Published 14 October, 2026

DOI: https://doi.org/10.1103/zrk4-g7fj

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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Phys. Rev. Research 8, 043048– Published 14 October, 2026
  • Received 7 July 2026
  • Accepted 2 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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