Assessing Reactive Responses and Gathering Restrictions for Eradicating Epidemic Diseases on Networks with Higher-Order Interactions

We characterize the dynamics of epidemic disease propagation on realistic temporal networks, where individuals participate in both pairwise and higher-order interactions. The latter captures large gatherings that may lead to superspreading events. We introduce an analytically tractable mathematical model for these temporal networks, based on continuous-time activity-driven networks, and study a susceptible–infected–susceptible (SIS) model spreading on its fabric. Utilizing a mean-field approach, we derive a system of ordinary differential equations (ODEs) that dictate the mean dynamics of the SIS process. By analyzing these ODEs, we identify the epidemic threshold of the model-revealing a phase transition between a regime where trajectories converge to a disease-free equilibrium and one where they stabilize at an endemic equilibrium (EE)-and delineate the unique EE for homogeneous networks. Subsequently, we integrate two distinct control measures into the model: i) restricting gatherings and ii) promoting a reactive behavioral response. We evaluate the efficacy of these control measures by computing the epidemic threshold of the controlled SIS model and employing various tools, including sensitivity analysis, mathematical optimization, and numerical simulations, to quantitatively assess how the control measures elevate the threshold, thus aiding in disease eradication, and how to amalgamate them for designing an optimal control policy.