Dynamic Modeling And Analysis Of Two Kinds Of Network Infectious Diseases

In our real life,many complex systems can be modeled as complex networks such as social networks and computer networks.In the past few years,a great deal of research has been conducted on the dynamics of transmission of infectious diseases on complex networks.Most of the studies on infectious diseases assume that the disease has only one form of ex-pression.However,in the real world,many infectious diseases are caused by multiple strains.And the interaction of humans and other behavioral effects on the study of infectious diseases also have a great impact.Therefore,this paper studies the modeling and analysis of dynam-ics of two-stage infection with competitive multi-strains and birth-death on heterogeneous networks.The first chapter introduces the practical significance of research on infectious diseases and the role of complex networks in the study of infectious diseases.The current research s-tatus of two kinds of infectious diseases in heterogeneous networks is also introduced.Finally,the basic knowledge used in this study is introduced.The second chapter mainly introduces the mathematical modeling and analysis of a completely competitive multi-strain disease.We established a multi-strain SIS model without a standard network and studied the dynamic changes of multi-strains with the mean-field method.It is proved that the disease-free equilibrium is globally asymptotically stable when₀<1.It is proved that the equilibrium with the largest basic number of regenerations is globally stable.Our results show that the principle of exclusion also applies to multi-strain disease.In the third chapter,in order to explain the human behavior in the social network,a two-stage epidemic model with birth and death and its dynamic analysis are established.Due to the dissemination of information and personal awareness,the infected individual gradually restricts his behavior or is isolated.As a result,the infectiousness changes from being dependent on degree distribution to constant.Therefore,the infectious disease is divided into two stages to establish the model.The effects of different infectious and birth and death on the epidemic dynamics were examined,and behavioral explanations of the number of basic breeds were conducted.And it is proved that the global equilibrium of disease-free equilibrium is asymptotically stable when₀<1.The positive balance continues for₀>1.The results show that human behavior has a significant impact on the spread of infectious diseases on the Internet.The fourth chapter summarizes the main conclusions of this paper and puts forward some ideas that can be further studied later.