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.

高阶交互广泛存在于现实世界的网络中，并极大地影响系统的相变和临界现象。在高阶网络上的流行病传播动力学研究中，不连续相变和双稳态物理现象引起了众多学者的关注。然而，流行病很少单独传播，而是在高阶网络上传播，从而使多种流行病相互影响。在高阶网络上促进传输的动力学仍然缺乏研究。本文探讨了单纯复形中两种流行病的协同传播，同时包括结构和动力强化效应。我们使用马尔可夫链和平均场方法来预测爆发规模和阈值以进行理论分析。增加结构或动力强化效应，促进传播动力，即爆发规模更显着，阈值更小。当两种强化作用较强时，系统会出现不连续的相变和滞后回线，较大的初始种子大小会导致疫情容易爆发。对于较大的初始种子大小，动态强化效应在大多数情况下会影响爆发大小。