Establishment And Analysis Of Rumor Spreading Model Of Uncertain SIAR

With the advancement of science and technology,Internet technology has explosively developed.Information can be spread directly and quickly to all corners of the world.As a kind of information,rumors spread on a wider scale and faster.Rumors usually refer to unsubstantiated and offensive statements.If rumors spread uncontrollably on a large scale,they will have a certain negative impact on social morals and order.Therefore,it is particularly important to establish an appropriate mathematical model for the analysis and research of the spreading process of online rumors.Most of the classic rumor spreading models are established on the basis of epidemiological spreading theories,with the establishment of deterministic rumor spreading models as the main research content.However,there are many uncertain factors in the process of handling the spread of rumors,and scholars often ignore the influence of these uncertain factors for the convenience of modeling.This thesis uses the Liu process to describe the uncertain factors in the spread of rumors.By analyzing the rumor spreading mechanism in different states,we established a rumor spreading model in the corresponding uncertain environment,and each influencing factor of the rumor propagation process is analyzed and numerically simulated in detail.The main tasks are as follows:(1)We believe that a person who has not heard of the rumors,after hearing the rumors,may continue to spread the rumors,may be uninterested in the rumors and remain silent,or may disagree and oppose the rumors.Based on the above mechanism,we established a SIAR rumor spreading model with opponents.By introducing the uncertain process,the uncertain SIAR rumor propagation model under the opposition mechanism is further obtained.The existence and uniqueness of the model solution is analyzed by using the uncertainty correlation theory,and it is explained that the model solution is stable according to the inverse distribution.Through numerical simulation,we found that as the rumor spreads further,the entire rumor spreading system will stabilize after a certain period of time.The number of communicators reached a peak over time,and then began to decline to zero,when the rumors stopped spreading.Due to the addition of opponents,the time for the rumor spreading process to reach stability has been reduced.(2)Based on the uncertainty of the SIAR rumor dissemination model,considering that some people may not immediately spread the rumors after hearing the rumors,but first show a state of hesitation to the rumors.The population is divided into five categories,namely,ignorant,spreader,opponent,hesitator,and immune,and a new model of rumors dissemination of uncertain SHIAR has been established.We prove the existence,uniqueness and stability of model solutions.Through the numerical simulation of the model,it can be found that although the addition of hesitators has an inhibitory effect on the spread of rumors,it also increases the time for the number of disseminators to stabilize,thereby increasing the time for the rumors to disappear.