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We develop a series of mathematical models to describe flow of information in different periods of time and the relationship between flow of information and inherent value. We optimize the diffusion mechanism of information based on model SEIR and improve the diffusion mechanism. In order to explore how inherent value of the information affects the flow of information, we simulate the model by using Matalab. We also use the data that the number of people is connected to Internet in Canada from the year 2009 to 2014 to analysis the model’s reliability. Then we use the model to predict the communication networks’ relationships and capacities around the year 2050. Last we do sensitivity analysis by making small changes in parameters of simulation experiment. The result of the experiment is helpful to model how public interest and opinion can be changed in complex network.

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 [

With the development of human society, information transmitting media is evolved continually. Meanwhile, morphology, structure and characteristics of the human society network are also in constant change. The flow of information is influenced by many factors such as inherent value of information, degree distribution of nodes and so on. So we are required to explore the evolution of the methodology, purpose, and functionality of society’s networks by analyzing the relationship between flow of information and inherent value of information and analyzing how public interest and opinion can be changed through information networks.

1) Given the complexity of calculation, we assume that information spreads on the small-world network. The small world network model is an actual complex network model which is located between the rules and random. Interpersonal relationship network as an example, most relationships may “short-range”, similar to the adjacent edges of the rules of the network model; many also have the distance relationships, similar to the remote jump edge [

2) The basic form of information diffusion is in accord with that of epidemic spreading. In this paper, we assume that the basic form of information diffusion conforms to SEIR model.

In SEIR model, people are divided into four classes [

・ The susceptible (S), who are susceptible to infection;

・ The exposed (E), who are affected but in the incubation;

・ The infectious (I), who are infected and have the symptom;

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

The total population of the area is N, and

In this paper, first we optimize the diffusion mechanism of information based on model SEIR. We think that the exposed can be changed to the recovered with a probability. Second, another two factors are involved in our model: the effect of information value and the degree of nodes. We think information value has influence on the exposed and the degree of nodes has influence on information diffusion. So the effect of information value represents the probability with which the susceptible could be changed to the exposed. In the other hand, the degree distribution of nodes can be added to dynamic equations of information diffusion. Meanwhile, the degree distribution of nodes can reflect how network changes over time.

We optimize the diffusion mechanism of information based on SEIR model and the improved diffusion mechanism is shown as follows:

・ After the initial node releases the information, the susceptible has three transition states. First the susceptible could be changed to the exposed with the possibility

・ The exposed could be changed to the infectious with the possibility

・ The infectious can be changed to the recovered with the probability of recovery

・ The recovered can be changed to the infectious with the probability of recovery

The flow chart of information diffusion is shown as follows (

The effect of information value reflects in two aspects: the importance of the information for people and time effect of information. The effect of information value can represents the probability with which the susceptible could be changed to the exposed:

When we do not take the degree distribution of nodes into account，the dynamic equations of the improved SEIR model are displayed below:

where

However, in fact information spreads on the complex network. According to assumptions, we regard the complex network as a homogeneous network. In addition, the degree distribution of the homogeneous complex network and mean-field theory is^{ } [

where

As a result, we establish final dynamic equations about density fluctuation based on Equations (4) and (5):

constraint condition:

where

In order to explore how inherent value of the information affects flow of information, we simulate the model by using Matalab. The values of parameters are as follows:

By changing the value of

From the results, we can get some conclusions:

・ With the increase of

・ With the increase of

In this paper, we define that the value added of people connected to Internet is the same as peak value of E. Because according to the two conclusions above, peak value of E means the number of people who are willing to connect to Internet to obtain the information whose

The data is about the number of people connected to Internet in Canada from the year 2009 to 2014 [

According to the results, the value of

According to model’s reliability analysis, in order to predict the communication networks’ relationships and capacities around the year 2050, we have to predict every year from 2014. The results are shown in

Time | Real value (R) | Prediction value (P) | |
---|---|---|---|

2009 | 28134809 | 27439705 | 2.47% |

2010 | 28546792 | 28064693 | 1.69% |

2011 | 29037081 | 28912343 | 0.43% |

2012 | 29673082 | 29512556 | 0.54% |

2013 | 31456390 | 30857157 | 1.90% |

2014 | 32090513 | 31603864 | 1.52% |

Time | Prediction value (P) | Time | Prediction value (P) |
---|---|---|---|

2015 | 32807310 | 2035 | 50006390 |

2016 | 33667264 | 2036 | 50866344 |

2017 | 34527218 | 2037 | 51726298 |

2018 | 35387172 | 2038 | 52586252 |

2019 | 36247126 | 2039 | 53446206 |

2020 | 37107080 | 2040 | 54306160 |

2021 | 37967034 | 2041 | 55166114 |

2022 | 38826988 | 2042 | 56026068 |

2023 | 39686942 | 2043 | 56886022 |

2024 | 40546896 | 2044 | 57745976 |

2025 | 41406850 | 2045 | 58285930 |

2026 | 42766804 | 2046 | 59465884 |

2027 | 43126758 | 2047 | 60395838 |

2028 | 43986712 | 2048 | 61185792 |

2029 | 44846666 | 2049 | 62045746 |

2030 | 45706620 | 2050 | 62905700 |

2031 | 46566574 | ||

2032 | 47426528 | ||

2033 | 48286482 | ||

2034 | 49146436 |

So we can know the number of nodes will reach 62,905,700 and the capacity of flow of information is doubled.

We make small changes in parameters by simulation experiment and find that

・ We can learn that when

In this paper, we propose a novel approach to organic SEIR model based on complex network topologies. By analyzing and simulating the different factors that affect the flow of information spread, we can get the relationship between flow of information and inherent value of the information.

1) Based on the experiments, the dynamic evolution of density fluctuation is simulated. The four dynamic equations reflect how the density of nodes in four different states varies over time. In the spread process, we conclude the main parameters by simulation experiment and find that

2) Furthermore, we need to determine how information value, people’s initial opinion and bias, form of the message or its source, and the topology or strength of the information network in a region, country, or worldwide could be used to spread information and influence public opinion.

This work was supported by the National Natural Science Foundation of China (71540028, F012408), and Major Research Project of Beijing Wuzi University. Funding Project for Technology Key Project of Municipal Education Commission of Beijing (ID: TSJHG201310037036); Funding Project for Beijing key laboratory of intelligent logistics system (No: BZ0211); Funding Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges Under Beijing Municipality (ID: IDHT20130517); Funding Project for Beijing philosophy and social science research base specially commissioned project planning (ID: 13JDJGD013); Beijing Intelligent Logistics System Collaborative Innovation Center.

Xiaocun Mao,Tingting Dong,Meng Li,Zhenping Li, (2016) Measuring the Evolution and Influence in Society’s Information Networks. Journal of Applied Mathematics and Physics,04,677-685. doi: 10.4236/jamp.2016.44078