Cooperative epidemic spreading in simplicial complex

Higher-order interaction exists widely in real-world networks and dramatically affects the system's phase transition and critical phenomena. In the study of epidemic spreading dynamics on higher-order networks, the discontinuous phase transition and bistable physical phenomena have attracted the attention of many scholars. However, epidemics are rarely spread individually but are spread on high-order networks so that multiple epidemics interact mutually. The dynamics of promoting transmission on higher-order networks still lack research. This paper explored the cooperative spreading of two epidemics in the simplicial complex, which simultaneously includes structural and dynamical reinforcement effects. We use the Markov chain and mean-field methods to predict the outbreak size and threshold for theoretical analysis. Increase the structural or dynamical reinforcement effect, and the spreading dynamics are promoted, i.e., a more significant outbreak size and smaller threshold. When the two reinforcement effects are strong, the system will have a discontinuous phase transition and hysteresis loop, and a large initial seed size will lead to the easy outbreak of the epidemic. For the greater initial seed size, the dynamical reinforcement effect affects the outbreak size in most cases.