Research On SIR Rumor Spreading Model In Uncertain Environment

With the development of the era of big data,there are more and more sources for people to obtain information,and more and more ways to spread information.Rumor spreading is a very important form of communication,which will bring great harm to people’s life and society.Rumors are not certain in the process of spreading,and will be affected by many factors in the environment.Most of these factors are uncertain disturbances.When there are enough data,probability theory can be used to study these uncertain disturbances.However,in real life,the acquisition of rumor data is very limited.Therefore,this thesis uses the new branch of mathematics uncertainty theory to study the process of rumor spreading,analyzes the inherent laws of rumor spreading,and gives some suggestions to control rumor spreading.This has important theoretical and practical significance for human development and social stability.Firstly,this thesis according to the idea of the classical DK model,the forgetting mechanism is added to the deterministic SIR rumor spreading model,and the Liu process is used to represent the uncertain disturbance in the environment.The probability of not spreading rumors rate in the deterministic SIR rumor spreading model is transformed into the uncertain variable which disturbed by uncertain factors,and the uncertain SIR rumor spreading model with a Liu process is established.Then the existence,uniqueness and stability of the solution of the model are analyzed.The α-paths of the model is obtained by Euler numerical algorithm.The influence of different parameters in the uncertain SIR rumor spreading model is analyzed.The results show that the rumor spreading rate,rumor avoidance rate,rumor forgetting rate and the intensity of Liu process have significant influence on the rumor spreading.The smaller the spreading rate is,the faster the rumor dissipates,the larger the forgetting rate and avoiding rate are,and the smaller the rumor scale is.In this thesis,the idea and method of multi-factor uncertain differential equation in uncertainty theory are used to extend the uncertain SIR rumor spreading model.People who know the truth of the rumor are added to the system,and the uncertain disturbance is also introduced to the spreading rate of the model.An uncertain SITR rumor spreading model with two independent Liu processes is established.By using the existence,uniqueness and stability theorem of the solution of the uncertain differential equation,the solution of the model is studied.Finally,through the numerical simulation,it is found that when other parameters are fixed,the initial value of the real information spreaders has a significant impact on the peak value of rumor spreading.The larger the spreading of people who know the truth of rumors in the system,the smaller the maximum value of spreaders,the smaller the impact of rumors.Therefore,the government can reduce the contact rate between the ignorant and the spreaders,and increase the number of people who know the truth of rumors by increasing the popularity of scientific knowledge,so as to reduce the scale of rumors and decrease the influence of rumors.