Emergent dilemma and periodic oscillation in the nonlinear interplay between epidemic and behavior

Abstract

Human behaviors, particularly non-pharmaceutical interventions (NPIs), are dynamically coupled with epidemic spreading. While prior studies mainly assume a linear interplay, real-world behavioral evolution is driven by nonlinear responses and social influence. Here, we incorporate these multifaceted mechanisms into a co-evolutionary model and analytically derive the critical thresholds. Notably, as the infection rate grows, NPI compliance initially rises but then abruptly drops to zero. This paradoxical decline indicates an emergent social dilemma: at high infection rates, abandoning NPIs is individually optimal but detrimentally triggers an explosive surge in epidemic prevalence. We further show that socially induced overestimation of the infection rate can counterintuitively prompt individuals to abandon NPIs. Moreover, the interplay with social influence induces periodic oscillations, reflecting a tragic cycle of recurrent epidemic waves. Furthermore, we validate the robustness of this NPI-abandonment dilemma in networked population. Our work illustrates rich emergent phenomena in the co-evolution of epidemic and behavior, challenging traditional views on this coupled dynamics.