Dynamics Analysis Of Several Types Of Rumor Spreading Model

In the age of web information, people are using electronic media more and more frequently. The way of people’s information communication is more convenient and information transmission speed is much faster. The blog, wechat and QQ has become the main online social interactions. Rumor as a kind of important form of social communication, it is a new media as the communication platform and its spreading has a significant impact on people’s lives. How to effectively control the spread of rumors and maintain people’s life and work in good order has become an important issue of social concerns. In this paper, we consider the nonlinear spread rate, stage structure and correct information intervention mechanism based on the classical SI (spreader-ignorant) model to study rumor spreading. We propose two types of rumor spreading models to analyze its dynamic behavior. We get the basic reproduction number and equilibria. We mainly study the stability of the equilibria. Numerical simulation examples are given to show that the correctness and effectiveness of the results in this paper.This paper mainly consists of four chapters.In the first chapter, we introduce the background of rumor spreading model, and summarize the current research progress of the rumor spreading models. Finally, we simply expound the main works of this thesis.In the second chapter, we introduce the process of the spread of rumors and give several preliminary lemmas.In the third chapter, the stability problem of a class of rumor spreading model is investigated. In Section 3.1, we propose a modified rumor spreading model with nonlinear spread rate and stage structure. Firstly, the spreading threshold of the considered model is given and the equilibrium point characteristics of the model are discussed. Moreover, the existence conditions of rumor-free equilibrium and the positive equilibrium are given. In Section 3.2, linear matrix method and Lyapunov function method is used to analyze the local stability and global stability of the rumor-free equilibrium and the positive equilibrium. In Section 3.3, numerical sim-ulation examples are given to verify the correctness of the theoretical results. In the process of simulation analysis, by adjusting the value of conversion rate, we observe that the later spreaders have a great influence on the spread of rumors. This result tell us that we need to strengthen the control of such rumor spreaders in order to prevent the rumor of explosion.In the fourth chapter, a class of rumor spreading model with nonlinear spread rate and correct information intervention mechanism is investigated. In the process of the rumor broadcasting, there must be some faithful information complied. The faithful information must have some inhibiting effect on rumors. Thus, we propose a class of rumor spreading model with information intervention mechanism, give the threshold value for the spread of rumors and analyze the stability of the modified model. Finally, the strategy how to control the rumor broadcasting based on the simulation results is presented.