Research On Several Kinds Of Propagation Problems On Complex Networks

With the rapid development of science and technology,the world enters the “2.0era”,which leads to a series of issues,such as the explosion of information,the damage of environment,the risk of the public health and so on.In particular,due to the diversity of communication channels,when people communicate with others on public social platforms,it could cause unpredictable consequences,such as the breakdown of social platforms or social panic causing by the spread of rumors.Furthermore,the risk of the public health has attracted more attention of the public,especially how to model and propose the effective strategies to curb the diseases spreading.So,it is important to study the spreading process of information and epidemics.Complex networks,as the powerful tool to describe the complex systems,can accurately present the spreading process of information and contacts between individuals.Therefore,the study of the diffusion dynamics on complex networks is of more practical significance.According to the common social behaviors in real life,this paper establishes several kinds of propagation models on complex networks by means of Markov chain approach and mean-field approximation method,so as to explore the spreading process of opinions and epidemics,and the final scale of opinions and epidemics on complex networks.The main work is as follows.Firstly,considering that people may communicate with others through a single or multiple channels in real life,we establish an opinion diffusion model on two-layered interconnected network based on the Markov chain approach,and explore the impact of seed(initial)fractions of opinions,inter-layer linking patterns and linking number,and mass media on opinion diffusion dynamics and the final fractions.By calculating the analytical expression of the opinion fraction,we discover that the final fraction of the opinion on one layer is identical with that on the other layer,and mass media will promote the spread of the opinion that is in accordance with its own.Then,by Monte Carlo simulations,we verify the validity of the model and the correctness of the conclusions.Furthermore,we investigate the evolution of two opinions on three types of two-layered interconnected networks with four kinds of inter-layer linking patterns,and find some interesting conclusions,which in turn,explain some common phenomena in reality,such as “celebrity effect” and “online celebrity economy”.Then,according to the characteristics of asymptomatic infection on the spreading process of COVID-19,we introduce an epidemic model with delay on the social network using the mean-field approximation method.By the method of next generation matrix and the stability theory of differential equations,we calculate the basic regeneration number and analyze the stability of the system on the equilibrium.Then,we obtain the possible measures to control the spread of the epidemic through the analytical expression of the basic reproductive number.By simulations,we find that the way to curb the spread of COVID-19 is to increase the recovery rate and the removed rate,and cut off the connections between symptomatically infected individuals and their neighbors,as well as the connections between hub nodes and their neighbors.The proposed measures are in fair agreement with the measures the government took.Furthermore,based on the epidemic data of Wuhan from January 24 to March 2,we analyse the outbreak in Wuhan.Finally,taking the interaction between the spreading process of epidemics and information diffusion into consideration,we introduce a dynamic model on the dulplex network by the microscopic Markov chain approach,calculate the epidemic threshold of the model and investigate the diffusion of information and the spreading process of epidemics.Theoretical analysis reveals that the epidemic threshold not only relies on the network topology of the epidemic layer,but also depends on the value of information on the information layer and risk perception parameters caused by information.Monte Carlo simulations verify the effectiveness of the model,and present that information diffusion reduces the prevalence of the epidemic.Furthermore,the more sensitive an individual is to information,the less prevalent the epidemic will be.