Two Types Of Propagation Problems On Complex Networks

Disease transmission and rumor transmission are two types of propagation problems on complex networks.Research on disease transmission is earlier than rumor transmission,and the results are richer and more perfect.This paper focuses on the effect of the communi-ty structure on the basic reproduction number of an SIR(Susceptible-Infectious-Recovered)model on complex network.Community structure is an important topological feature of complex networks.There are many research results on the comrimnity structure.But so far,no one really answered the question of the effect of the community structure on the basic reproduction number of disease transmission.The result of this paper only partially answer this question.On the other hand,as a typical social phenomenon,rumors have not disappeared in modern society.But even the means and ways of rumor transmission have changed a lot.Therefore,it is very important to study the mechanism of rumor transmission.Due to there are many similarities between rumor transmission on the networks and epidemic transmis-sion,most rumor propagation models are based on infectious disease models.In this paper,the ISR(Ignorant-Spreader-Refractory)propagation pair models on the complex networks are established by using the pair approximation method to study infectious disease models,which extends the classical rumor propagation model.For the reasons given above,the paper not only uses the method of adjusting the ratio of inside and outside edges of the community to change the community structure and keep the total degree invariant,so as to study the effect of the comnunity structure oin the basic reproduction number,but also establishes the rumor propagation dynamics under two mechanisms by the approach of pair approximation and studies their similarities and differenees.This paper is divided into three chapters.In Chapter 1,we introduce some preliminaries,research background and main content.In Chapter 2,study the effect of the community structure on the basic reproduction number of an SIR model.We consider the SIR disease model in two-cemmunity complex networks with an arbitrary joint degree distribution,i.e.,(?)Then the basic reproduction number R0 of the model is calculated by the next generation matrix method.i.e.,(?)Then,we can get the basic reproductiol number R0 of the SIR model in the initial random configuration network further.i.e.,(?)Which agree with the basic reproduction number of a random network with no community structure.Next,the influence of community structure on the basic reproduction number is studied under the evolutionary mechanism introduced in Section 2.1.2.The conclusion shows that the basic reproduction number is not changed when the community structure is strengthened.In Chapter 3,the ISR rumor propagation model on a kind of complex network is es-tablished by the approach of pair approximation,and the influence of rumor propagation parameters on the propagation dynamics is studied by using numerical simulations.Finally,the similarities amd differences between rumor propagation mechanism and disease transmis-sion mechanism on complex networks are discussed.The conclusion are that:1.The emergence of this direct path from the ignorant to the refractory weakens the spread of rumors and makes the rumors end earlier.2.The scale of rumor propagation and the number of spreaders under the rumor propagation mechanism are lower than those under the disease transmission mechanism.