Competing Spreading Dynamics In Simplicial Complex

Diseases are widespread in nature.As the distance between people-to-people and people-to-animals is getting closer,epidemics which existed in nature for a long time can also spread in human society.Human society has been encountered by many epidemics,such as Black Death,Smallpox,Cov-19 and other deadly epidemics spread on a large scale in human society,and has caused a severe impact on industry,transportation,economy and medical treatment.It is found that the spread of the epidemic can be effectively controlled by means of ‘quarantine’.Therefore,the research on the spreading route and mechanism of the epidemic is extremely important.The idea of epidemiology is also applicable to spreading scenarios that are essentially similar to biological disease contagion.In this paper,we study the dynamics of propagation on complex networks from the perspectives of network complexity and dynamics complexity respectively.In the first part,based on the idea of epidemiology,we study the information diffusion structure in social networks with general degree distribution based on the simple graph theory.This part mainly studies the information diffusion structure of ER network with Poisson distribution and SF network with power-law distribution.Combining with the epidemic model,we model the spread of information with SIR model in two different degree distribution networks,and propose the measurement index of information diffusion structure.Then,combined with computer simulation,the information propagation on the network with two degree distributions is studied systematically from four aspects: threshold,cascade hierarchy,shortest path distribution and corresponding diffusion index.It is found that the law of information diffusion in SF network is similar to that in ER network.In the second part,we propose two competitive spreading models of SIS type epidemics on homogeneous mixed simplicial complex from the perspective of high-order interaction.In the model,the simplicial complex is used to describe the high-order interaction,and the evolution equation of the system is derived based on the mean field theory.The knowledge of nonlinear dynamics is used to analyze the fixed points of the system and the stability of each fixed point.The phase diagram of the system is obtained by combining analytical solution with numerical solution,and the results show complex critical behavior.Through a large number of numerical simulation experiments,it is found that the evolution process of the two epidemics is closely related to the initial node density of both sides.Finally,combined with the theoretical model and simulation,the outbreak size of the epidemic is predicted,and the results show that the simulation results are basically consistent with the theoretical results.