Research On Epidemic Spreading Mechanism Based On Complex Network

Epidemic spreading on complex networks is an essential problem in the real world.The dynamics of disease transmission on complex networks are involved in the spread of infectious diseases in human social networks,virus attacks in computer networks,and the outbreak of financial crises.Studying the regulation of epidemic spreading on complex networks and making corresponding prevention and control strategies are the key to preventing disease outbreaks and reducing economic losses.This thesis realizes that the infection threshold of disease is critical in epidemic spread.It affects the scale of epidemic outbreak size and the critical condition of disease spreading.Traditional epidemic spreading models usually assume that individuals have the same infection probability,which is helpful to simplify the analysis of disease transmission but conflicts with the actual situation.At the same time,individuals have their friend circle and can provide support with flexible resources(time)and medical resources(masks).Considering the heterogeneity of individual infection threshold,the limitation of neighbor resources in the network,and individual immune characteristics,this paper studies disease transmission on complex network.The main research contents are divided into the following two points:(1)For the disease network supported by neighbor resources,Gaussian distribution was used to describe the infection threshold heterogeneity of individuals in the network.Transmission dynamics and complex network theory are used to study and analyze the transmission process of infectious diseases in single-layer biological networks.This thesis proposes a generalized Susceptible-Infected-Recovered model with the heterogeneity of infection threshold and the support of neighbor resources to qualitatively analyze the transmission process of the disease in the network.It is found that increasing the mean value of the normal distribution parameters of the infection threshold can inhibit the transmission of the disease under certain conditions.And appropriately increasing variance can promote the spread of disease in the network.The scale of disease outbreaks can be better controlled if the resource-sharing index is zero.(2)For the single-layer biological networks with individual immune characteristics,this thesis studies and analyses the transmission process of infectious diseases in single-layer biological networks based on transmission dynamics and complex network theory.This thesis proposes a staircase function to represent the relationship between individual infection probability and infection frequency in the network using the Susceptible-Infected-Recovered model.The edge division method is improved for theoretical analysis.It is found that changing the initial infection threshold or the time interval of the infection threshold will cause the phase transition of the system since fewer and fewer nodes reach a certain infection probability in the network and the number of subcritical nodes increases significantly.In addition,with the increase of heterogeneity,the epidemic outbreak size eventually changed from a continuous phase transition to a discontinuous phase transition.