Analysis Of Several Dynamic Models On Scale-free Networks

Throughout the history of mankind,it can be found that from the birth of mankind to the 21st century,we have overcame countless infectious diseases,However,with the continuous evolution and mutation of viruses,various infectious diseases still emerge in an endless stream.Nowadays,the spread of infectious diseases poses greater harm to the safety of people’s life and property and the sustainable development of the country.This is because,with the development of the transportation network extending in all directions,the links between countries,cities and cities have become closer.Urbanization has also led to a more crowded and dense society and become a hotbed for the spread of infectious diseases,thus accelerating the globalization of infectious disease spread.At the same time,the 21st century is also the era of the rapid development of the Internet.In the new era,the channel of information transmission is no longer simply the transmission of offline,but more transformed into a social network platform.Cross-regional social platforms have accelerated the spread of different information in the world.From the perspective of the above infectious diseases and information transmission modes and changes in transmission routes,it is even more necessary to carry out in-depth research on the dynamics of infectious diseases transmission and information transmission mechanism.Considering the factors affecting the spread of infectious diseases in reality,combined with the network topology of scale-free networks,this paper establishes a dynamic model of infectious disease transmission based on scale-free networks,specifically analyzes the dynamic behavior of infectious disease transmission in the population,and studies the specific performance of the factors affecting the spread of infectious diseases.In addition,from the two dimensions of live streaming commerce spreading and network fraud information transmission,according to the scale-free characteristics of social networks and the differences of individuals,the live streaming commerce model and network fraud information spreading dynamics model are established respectively,and the information spreading on social platforms is carefully analyzed.The innovation and research work of this paper mainly includes the following three aspects:1、In order to explore the impact of the detection rate and the vaccination rate on the spread of infectious disease in detail.A new dynamic model of pandemic spreading based on scale-free network is proposed,namely SMADRHV model.On the basis of the warehouse model,according to the mean field theory,combined with the next generation matrix method,the basic reproductive number of the SMADRRV model is obtained.At the same time,it is proved that there is a disease-free equilibrium point in the system at time R0<1,and there is an equilibrium point for the continuous spread of infectious t diseases at time R0>1.point and the persistence of the dynamic behavior of infectious disease transmission are also studied in detail.Finally,the model is simulated,and it is found that "early detection" and improving the vaccination rate of the population have certain effectiveness in controlling the spread of infectious diseases2、The SPCGF(Susceptible-Potential viewers-Consumer-Gainer-Follower)model is firstly abstract based on the actual situation with the purpose to specifically understand the live streaming commerce mode,explore the influence of the anchor’s reputation and the quality of the commodities.And The model of information transmission is studied in the following three aspects:① According to the mean field theory,combined with the next generation matrix method,the basic reproductive number R0 of the system is obtained,and the existence of the relevant equilibrium point is proved.② According to Perron-Feobenius theorem and Lajmanovich and York lemma,the stability of the model and the persistence of dynamic propagation behavior are proved.③And the influence of related factors on the spreading behavior was also discussed.It is found that improving the popularity of the anchor and the quality of the goods in the live broadcast room can promote the continuous development of the live broadcast shopping mode to a certain extent.3、In order to control the spread of online fraud information,explore the specific influence strengthening anti-fraud publicity and strengthening the supervision of false fraud information on online platforms,the SBVR(Susceptible-Believer-VictimResistant)online fraud model is put forward.Further,the basic regeneration number and the equilibrium point of the disappearance of fraud information and the equilibrium point of the persistence of fraud information is obtained through mathematical analysis.Secondly,the stability of the model and the persistence of dynamic propagation behavior are proved according to relevant theories.Finally,the numerical simulation of theoretical analysis is carried out,and the influence of relevant parameters is simulated.It is found that strengthening the anti-fraud propaganda and strengthening the information supervision on the network platform have practical benefits to prevent the occurrence of network fraud and curb the spread of network fraud information.