Research On The Spread Of Epidemic On The Community Network

Zhang YunApplied MathematicsDirected by Yang JinxuanComplex systems can be represented by complex networks,many of which have a common community structure.The spread of epidemics in community networks has always been one of the key contents in the study of epidemic spreading dynamics on complex networks.The process of epidemic spreading in multi-layer network with community structure is quite different from that in single-layer network.First,epidemic spreading with evolving community structure is studied,and then the spreading dynamics model of SIR and SIRD epidemics on a multi-layer network with community structure is explored.This thesis analyzes the epidemic spreading dynamics from two perspectives: epidemic threshold and outbreak of epidemic.The influence of population mobility on the spread of epidemics is further studied,and some strategies to prevent and control the spread of epidemics are put forward.The specific research content is provided as follows:Firstly,the mean-field method is utilized to obtain the epidemic spreading dynamics model of community structure evolution.Changes in the spread of epidemics as communities emerged or disappeared,grew or contracted,divided or merged are further analyzed.Theoretical analysis shows that the emergence of new communities leads to lower epidemic thresholds and increased infected individuals.Conversely,the disappearance of communities helps raise epidemic thresholds and slow the spread of epidemics.The contracting community size leads to higher epidemic thresholds.The division of communities leads to an increase in epidemic thresholds and a decrease in infected individuals.In other words,in the real-world network with community structure,individual isolation in the community will lead to an increase in the epidemic threshold,thus slowing down the spread of epidemics.The numerical simulation results are in agreement with the theoretical analysis.Secondly,this section studies the spread of epidemics on homogenous evolutionary networks,including population mobility and demographics.The results show that population mobility affects the epidemic threshold in each community.Controlling outbreaks of epidemics in important communities is a good way to control the spread of epidemics throughout the system.When a layer of the network is isolated,it is further found that the average degree within the community affects the epidemic threshold of the community.Therefore,isolating individuals in important communities can reduce the average degree within the community.The lower the frequency of contact between individuals,the higher the epidemic threshold,thus slowing the spread of epidemics.Finally,we propose a network evolution model,and give a multi-layer homogeneous network disease propagation dynamic model with community structure when it evolves according to the evolution model.By building the SIRD epidemic model,we found that reducing the average degree within a community or between two layers of networks can slow down the spread of epidemics.In other words,the reduction of the spectral radius of the community network leads to the increase of the global and local epidemic threshold,and thus slow down the spread of epidemics.