Activity feedback and hyperedge overlap shape bistability in higher-order networks.

Abstract

Behavioral feedback plays a crucial role in shaping epidemic dynamics. In this work, a contagion framework that combines higher-order interactions with a dynamic activity-feedback mechanism is developed and analyzed. An evolution equation describing the temporal dynamics of the activity rate is formulated under the assumption that group behavior is regulated by the current prevalence. Two different bistable states are identified, and the conditions for their appearance and disappearance are clarified. To assess the generality of these findings, we numerically simulated the framework on networks with different levels of hyperedge overlap. Numerical simulations further show that hyperedge overlap modulates the bistable window in a feedback-dependent manner and, under strong behavioral feedback, low-overlap networks can trigger a rapid decline in activity rate, thereby suppressing sustained outbreaks. These results provide a qualitative perspective for understanding behavioral-response patterns reported during the COVID-19 pandemic.