On a Susceptible-Infected-Susceptible Epidemic Model with Reactive Behavioral Response on Higher-Order Temporal Networks

We characterize the spread of epidemic diseases on higher-order temporal networks to shed light on the impact of large gatherings, where superspreading events occur and pairwise interactions are not sufficient to model the dynamics of infection. We propose a novel analytically-tractable continuous-time formalism for higher-order temporal networks based on the paradigm of activity-driven networks and we study a susceptible–infected–susceptible model spreading on top of it. By using a mean-field approach, we compute the epidemic threshold, characterizing a phase transition between a regime where the system converges to a disease-free equilibrium and one in which all trajectories converge to an endemic equilibrium. Using such a threshold, we quantify the role of higher-order interactions in favoring the spread of epidemic diseases, providing analytical support to restricting large gatherings during an epidemic outbreak. Finally, we incorporate a reactive behavioral response in the network formation process.