Noise-induced transients in the propagation of epidemic with higher-order interactions

During epidemic propagation governed by a susceptible-infected-susceptible process, infectious disease dynamics exhibit transients between stable equilibrium states. This study identifies noise as a key factor in inducing such transients, leading to an earlier onset of tipping points in both outbreak and recovery phases. A network epidemic model incorporating higher-order interactions is formulated, along with its reduced form. The impact of noise is examined separately for models with and without higher-order interactions. The results show that environmental noise advances epidemic outbreaks by lowering the tipping threshold, whereas demographic noise facilitates faster recovery transitions. Moreover, higher-order interactions amplify nonlinear feedbacks, widening the hysteresis between the outbreak and the recovery and prolonging transient durations. A theoretical framework is then established to describe the dependence of the mean transient time on noise intensity, highlighting the role of noise-induced transients in shaping epidemic thresholds and control strategies.