Competing spreading dynamics in simplicial complex

Interactions in biology and social systems are not restricted to pairwise but can take arbitrary sizes. Extensive studies have revealed that the arbitrary-sized interactions significantly affect spreading dynamics on networked systems. Competing dynamics, i.e., several epidemics spread simultaneously compete with each other, been widely observed real world, yet way competing still lacks systematic study. This study presents a model of two simplicial susceptible-infected-susceptible higher-order system represented by complex analyzes model’s critical phenomena. In proposed model, susceptible node only be infected one epidemics, transmission infection neighbors occur through (i.e., an edge) (e.g., 2-simplex) simultaneously. Through mean-field (MF) theory analysis numerical simulations, we show displays rich dynamical behavior depending 2-simplex strength. When strength is weak, phase diagram consistent simple graph, consisting three regions: absolute dominant regions for epidemic epidemic-free region. With increase strength, new region called alternative emerges. this region, survival depends initial conditions. Our theoretical reasonably predict time evolution steady-state outbreak size addition, further explore both when symmetrical asymmetrical. The results has significant impact diagram.