Dynamics of SIRS epidemic model in heterogeneous hypernetworks.
In this paper, the complex epidemic behavior of higher-order interactions is investigated by considering heterogeneous hypernetworks with collective contagion mechanisms, and a susceptible-infected-recovered-susceptible epidemic model is established in hypernetworks. First, we propose a mean-field model in heterogeneous hypernetworks based on hyperdegree and conduct analyses of this model. For general heterogeneous hypernetworks, we determine the epidemic threshold for disease spread and the threshold for the emergence of backward bifurcation, performing comprehensive dynamical analyses. Specifically, in a heterogeneous hypernetwork where the hyperedge size does not exceed 4, the existence of endemic equilibria is examined, and conditions for the system possessing a varying number of endemic equilibria are provided. By analyzing the model, we identify three types of bifurcations and two distinct bistable phenomena. Finally, theoretical predictions are confirmed through numerical simulations.