Step 1. Characteristic extraction [2]

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.

is the set of the neighbor node of u, is the set of the neighbor node of v.

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:

is a constant, is the weight of every characteristic.

Transmission probability can be calculated by Bayesian logistic function [3] :

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 and both nodes’ opinion intensity stay the same:

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 is utilized as an intensity factor of opinion. According to the process of opinion transmission, the characteristics of opinion intensification will finally show up on the probability of network transmission. We establish an equation as below to denote the effect of opinion intensification.

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 [4] (Online social network propagation modeling)

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.

Here we assume, then we observe how information spreads with the changes in which can reflects the change of public interests. And the results are as follows (see Figure 1 and Figure 2).

According to Figure 1, we can learn that as the coefficient of interest attenuation increases, the number of nodes in the state of R which can reflects the scale of information propagation decreases. So public interests have big influence on information propagation and interest attenuation can inhibit the spread of information effectively. That is to say, the attenuation mechanism of interest has negative correlation with the scale of information propagation. This result is in accordance with the conclusion which Nekovee put forwards [5] . Figure 2 shows the process of information propagation and it also confirms that the bigger the coefficient of interest attenuation is, the smaller the number of people who are more likely to spread information is.

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, then we observe how information spreads with the changes in which can reflects the change of public opinion intensity. And the results are as follows (see Figure 3 and Figure 4).

According to Figure 3, we can learn that as the reinforcement effect of opinions increases, the number of nodes in the state of R which can reflects the scale of information propagation also increases. So opinion intensity has big influence on information propagation and reinforcement effect of opinions can promote the spread of information effectively. Figure 4 shows the process of information propagation and it also confirms this law. In another hand, at the beginning or end of information propagation, information propagation is less affected by opinion intensity. But it influences information propagation probability apparently in the intermediate stages.

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.