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During the diffusion of information on the network, the users generally have such an experience that at the beginning they get aware of the news they never know and may be willing to inform others, then their interests fade away, finally the information stops flowing. Meantime, their points of view are changing as the networks’ structure changes. Therefore, this article brings in the interest attenuation mechanism and the social networks consensus evolution mechanism on the basic of the improved SEIR model. So to begin with, we establish a model to analyze how users’ interests change during the diffusion of information on the network. Second we establish another model to analyze the evolution of the opinion during the diffusion of information on the network. At last, we establish a final model by using dynamic equations adding the results of the two models above.

Information sharing is the basis of human society. A History of Communications advances a new theory of media that explains the origins and impact of different forms of communication on human history [

In our paper we establish two submodels and one master model based on SEIR model to solve this problem. First we establish an interest attenuation model and the main innovative point is that we use the coefficient of interest attenuation

・ Assumption 1. The users’ interests do not couple with their opinions.

・ Assumption 2. We regard the information attenuation characteristics as users’ interests attenuation characteristics. So the probability of interests attenuation can be denoted by P(the transmission probability of interest):

where p is the transmission probability of interest. It is also the function of information’s value, mode of propagation and the influence of node.

・ Assumption 3. There is only one source node in the network with others all healthy nodes at the initial state. At the beginning, every node has its own original opinion, and the distribution of these opinions is uniform.

・ Assumption 4. We assume that D represents the inclination of every node’s opinion, and D has three options including support, neutrality and objection. T is used to stand for the intensity of the inclination. T ranges from zero to one. Much closer to one, the T is means the degree of support intensity gets higher [

Step 1. Characteristic extraction [

Influence of node: the sum of all the messages’ influence that are released in a certain period from one node. Provided that #RT represents the times that the messages were republished, then the influence of node can be expressed as:

Characteristic of information: We use emotional attribute Sentic (C) to represent it. The message that has great emotional intensity tends to get spread more widely. Two-dimensional vector, positive and negative dimensions, can represent it. We will do some work with the eigenvectors to make the sum of all the components in the vector is one. We assume that x stands for the positive emotion score, y stands for the neutral emotion score and z stands for the negative emotion score. Hence, the eigenvector can be expressed as:

The form of information communication: the form of information communication relates to the structure of the network. This article employs two nodes’ p2p set Jaccard distance to denote the similarity of network structure.

Step 2. Model construction

Characteristic parameter is extracted, which can better reflect Interest attenuation, combining it into the feature vector

The basic function can be expressed by linear combination of eigenvectors:

Transmission probability can be calculated by Bayesian logistic function [

Therefore, the probability of interest attenuation is:

Step 1. Propagation model based on the modified SEIR

This model is similar to model 1, but the exposed will be influenced by interest attenuation and other users’ opinions. In addition, information spreads on the non-uniform complex network. So we can call the model ICSR so as to distinguish it from SEIR.

・ the susceptible (I), who are susceptible to infection.

・ the exposed (C), who are affected but in the incubation.

・ the infectious (S), who are infected and have the symptom.

・ the recovered (R), who recover or survive.

When users’ interests in information decline, they will stop diffusing information at the rate of ζ and then enter latent state. ζ is the target value of Interest Attenuation Model. When users’ opinions inclination become diversified, considering that events may have new progress, users will turn from latent state to opening state at the rate of ζ which is the target value of pinion evolution model.

Step 2. Opinion transmission process based on the modified SEIR model

According to Model 1, we employ the change of opinion intensity:

If the neighbor node j belongs to I, j will turn to S at the rate of β, and gets its opinion intensity recalculated.

At the same time, node j probably refuse to forward the message to others, and turn into immune state at the rate of α. Then, there will not be any difference in two nodes’ opinion intensity:

If the neighbor node j belongs to S, node i will stop diffusing message because of the decline of interest and turn into state C at the rate of ζ, while node j stay the same. The opinion intensity of node j will get updated:

If the neighbor node j stays at state C, considering that two nodes have different opinions on the same topic and will both trace the development of the event as the event may produce some new progresses, therefore, by the next point of time node j will become a transmitter at the rate of ζ, while both node i and node j will get their opinion intensity recalculated:

If the neighbor node j belongs to R, node i will turn into state R at the rate of

Step 3. The quantification of the effect of opinion intensification

According to Deffuant opinion propagation model, index T is used as opinion value. The difference in the inclination of opinions between different nodes decides that the nodes will turn into transmission state again or not. So, in this article

Based on the results of two models above, it has been taken into consideration that the change of users’ interests and opinions may affect the process of information propagation. Then we add these two factors into the dynamic equations of information propagation. As the information propagation network can be regarded as non-uniform complex network, these kinetics equations are established on the basic that epidemic is in the non-uniform complex network.

The dynamic equations have been given [

In addition, in the interest attenuation model and opinion evolution model, we can obtain that

So we can obtain the characteristic of information propagation on the basic of users’ interests and opinions by building simultaneous equations with this equation and four equations proposed above.

We can learn that information value and form of the message have influence on ζ. People’s initial opinion, bias and the topology or strength of the information network have influence on ζ. In addition the size of the network has influence on

In order to explore how people’s initial opinion and interests affect the topology or strength of the information network, we simulate the model by using Matalab. Then we use Originpro to process the data. The total number of nodes N is 10000. The values of parameters are as follows:

Here we assume

According to

In another hand, at the beginning or end of information propagation, information propagation is less affected by interest attenuation. But it influences information propagation probability apparently in the intermediate stages.

Here we assume

According to

According to the pictures and analysis above, we can obtain that the influencing mechanisms of the two cases are opposite. At the same time, the influence of the interest attenuation is stronger than that of opinion intensity.

First, the mechanisms of interest attenuation and the reinforcement effect of opinions both have great influence on information propagation and the two mechanisms are opposite.

Second, in the process of information propagation, they play different roles have different importance in different stages. So we can control information propagation by controlling the two factors in different stages.

Third, the influence of the interest attenuation is stronger than that of opinion intensity so we can control information propagation by adjusting the weights of the two factors.

This paper is supported by the Funding Project for Technology Key Project of Municipal Education Commission of Beijing (ID: TSJHG201310037036); Funding Project for Beijing key laboratory of intelligent logistics system; Funding Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges Under Beijing Municipality (ID: IDHT20130517), and Beijing Municipal Science and Technology Project (ID: Z131100005413004); Funding Project for Beijing philosophy and social science research base specially commissioned project planning (ID: 13JDJGD013).

Funding Project for Beijing Intelligent Logistics System Collaborative Innovation Center.

Juntao Li,Tingting Dong,Meng Li, (2016) Research of Social Network Information Propagation Model Based on Public Interest and Opinion. Social Networking,05,75-81. doi: 10.4236/sn.2016.52008