Higher Order Epidemic Spreading in Simplicial Networks

The spread of epidemics is a complex process influenced by multiple social relations, including families, schools, and companies. Group interactions represented by a simplicial complex have been shown to impact the dynamics of epidemic transmission significantly. However, the previously proposed higher order contagion models only consider the propagation process within the higher order structure but lack a description of the consistency of the node states in the structure. To address this problem, we provide solutions to create a solvable network model that shows network clusters and node state consistency tendencies, capable of capturing the coexistence of interacting groups. We analyze the bistable region and epidemic threshold of the higher order propagation dynamics and explore the effect of the state update of the nodes on the model in: 1) random regular simplicial networks; 2) triangular simplex-lattice networks; 3) star-simplicial networks; and 4) heterogeneous simplicial networks. Our theoretical analysis, complemented by Monte Carlo numerical simulations, demonstrates that the proposed model accurately captures phase transitions and the bistable region created by higher order interactions. In addition, we find that the incorporation of intersimplex interaction mechanisms greatly reduces the epidemic threshold of the system and produces a larger bistable region, in which the dynamics of the system are heavily affected by the density and location of the initially infected nodes. Our findings contribute to a better understanding of higher order interactions in complex networked systems.