Stability Analysis Of An SIRS Model With Time-delay On Scale-free Network

It is easy for the study of the propagation process of many infectious diseases to obtainconclusions by the analysis of complex dynamic networks. Many SI, SIS and SIR models onScale-Free Networks are analyzed accurately. Due to the speed of information transfer ormemory, delay often occurs in many complex networks. In this paper, SIRS model with delayon Scale-Free Networks is researched.In chapter one, we introduce the study significance of the paper, and the development ofmodels on Scale-Free Network.In chapter two, we introduce common knowlege of infectious diseases, for example, thedynamics of homogeneity infectious diseases, the basic reproduce number; then, we explainsimple knowlege about complex network, such as, degree and degree distribution, Scale-FreeNetwork, and modelling of infectious diseases on network;finally, we present simplely therelevant theoretical knowledge that need to use, for example, the theory of persistence.In chapter three, we investigate an SIRS model with time delay on the uncorrelatedScale-Free Networks, and analyze the dynamical behavior of the model. We give theexpression of the basic reproduction number by considering the existence of the endemicequilibrium.By constructing Jocabi matrix and Lyapunov function, the global stability of thedisease-free equilibrium is proved. Finally, the persistence of endemic equilibrium isobtained.In chapter four, based on the model of chapert three, we present an SIRS model withtime delay and saturated link on the uncorrelated Scale-Free Networks. The basicreproduction number and the unique endemic equilibrium of this model are obtained. By constructing Jocabi matrix and Lyapunov function, the global stability of the disease-freeequilibrium is proved.