Research Of Epidemic Spreading Dynamics And Control Strategies On Scale-free Networks

Since the concept of complex networks was proposed,scientists have never stopped studying the propagation dynamics behavior of various complex networks.It can well describe the various phenomena formed by the interconnection and interaction of a large number of individuals in various disciplines and fields,and with the help of complex network related knowledge,it is conducive to better understanding the propagation law of these communication phenomena,so as to effectively control their propagation process.The heterogeneity of scale-free networks is more in line with reallife community networks,so the proposal of scale-free networks has brought the research of complex networks to a new level.Infectious diseases have always threatened people’s health and even had a great impact on the social economy.Therefore,the study about infectious disease transmission dynamics has gradually become a research hotspot for experts in the field of complex networks.In order to study the transmission mechanism of infectious diseases so that the best control strategies can be developed,experts have begun relevant theoretical research work.How to formulate measures to prevent the widespread and rapid spread of infectious diseases has important reference significance and practical value for society,so it is very important to study the transmission dynamics of infectious diseases.Based on the scale-free network,according to the transmission characteristics of infectious diseases and some important factors,several suitable transmission dynamics models for the spread of infectious diseases are established,and detailed research and analysis are made on these models,the key factors affecting the spread of infectious diseases are analyzed,and corresponding solutions are proposed according to the analysis results.The specific research content and novelty of this article probably include the following aspects:1.In order to explore the influence of early hospitalization and vaccination on the transmission of infectious diseases,a class of SEAIHRV infectious disease transmission models are proposed under the background of scale-free networks.In the research process of this model,in terms of its dynamic behavior,detailed and in-depth analysis was carried out,including the solution of the basic regeneration number,the verification of the equilibrium point,and the proof of stability.In addition,the attractiveness of the endemic equilibrium point was also demonstrated by the iterative method.Finally,through simulation,the theoretical results are verified.2.Considering the influence of the strong contagiousness of superspreaders on the spread of infectious diseases,a type of SEMIQR infectious disease transmission model is proposed under the background of scale-free network.By using the mathematical theoretical analysis,the basic regeneration number of the model is calculated,and the disease-free balance point and endemic equilibrium point are obtained.The global progressive stability of the equilibrium point,the persistence of infectious disease transmission and the global attraction of the positive equilibrium point are proved,and numerical simulation is also used to verify it.3.Considering the impact of low-risk groups on the spread of infectious diseases under self-protection mechanisms(such as wearing masks,maintaining a certain social distance,home isolation,etc.),a type of SLEIR infectious disease transmission model is proposed under the background of scale-free networks.At the same time,in terms of its dynamic behavior,a detailed and in-depth analysis is carried out,including the solution of the basic regeneration number,the verification of the equilibrium point,and the proof of stability.The theoretical results are verified by numerical simulation.