A SEIR Model Epidemic of Virus on the Online Social Network

By Min, Yang; Qianmu, Li et al. | Journal of Digital Information Management, April 2014 | Go to article overview

A SEIR Model Epidemic of Virus on the Online Social Network


Min, Yang, Qianmu, Li, Yaoliang, Song, Journal of Digital Information Management


1. Introduction

There are a lot of ways that the spread of computer viruses on the Internet, such as email or the sharing of Peer - to Peer file etc. In recent years, as the number of the service (SNS, hereinafter referred to as the social network) users are growing at a very fast rate; it also provides a new route of spread of the virus. Facebook, the number of Twitter and domestic renren and weibo or other social network 'users are increasing; social network is gradually changing people's life. People can communicate and share files on social networks, even interacting with friends through other platforms that the social networks provide. These convenient services, however, also give the virus more opportunities to infect users. Once a user is infected with the virus, the virus will be automatically sent to the other users who are on this user's friends list. Virus on the Social networks can be dangerous links or videos, etc. As a result, the speed of the spread of virus on the social network is very fast. At the same time, most of the social network users upload their personal information, so the viruses of the social network are more likely to affect the user's privacy and personal safety.

In view of the virus propagation on social networks, some scholars have already carried on the related research. Reference [1] studied virus propagation model based on the email, assuming that the viruses spread when the users click the E-mail attachments. Experiments have proved that if the users see their email in irregular time, the virus will spread faster. Kominos considered that user's behavior will change over time, such as the probability of opening old email attachments is small, as a result he proposed IM and P2P worm propagation model which spread via email. After studying the propagation law of viruses on Facebook, Fan proposed two models. One is based on the application platform on Facebook and another one is based on sending messages to friends.

But the models above have some limitations. First of all, the viruses that spread on the online social network are more complicated than the viruses that spread by email and IM Network. Secondly, users have their own behaviors, such as online time. Most users are not always online. As a result, user's online status has a crucial effect on the spread of the virus. So the online social network virus propagation model must consider a key factor--user's login interval.

Anderson and May add status E to the SIR virus propagation model, and put forward a SEIR model [2]. SEIR model is more detailed and true when it simulate the spread of the virus.

In this paper, the main works are as follows.

(1) Explained the propagation theory of virus spreading on the social networking [3].

(2) Put forward SEIR virus propagation model based on online social networks.

After have analyzed the interval of logging, the number of friends in the users' friends list and the influence of the virus's initial spreading rate during the propagation process of the virusythe simulation experiment has proved the effectiveness of this model.

2. Description of the model

The structure of XWLB is firstly analyzed first and then story type is concluded in this section.

2.1 Virus Propagation Mechanisms of the Model

Researchers have found that the topology of the famous social networking such as Facebook is undirected graph structure. The topology of undirected networks can be shown by forms. Every node in the form stands for a user in the Internet. If node i and node j have a connection side, they have each other in their list of friends [4]. The model defines that every node's degree is the number of users in the list of friends of the node.

In this passage, the model divides all the nodes into 4 statuses: Susceptible node S, infected node l, immune node R, and exposure node E. Among them, S status shows the node is healthy, but is likely to be infected by a virus [5]. …

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