Analysis Of SIR Model On Scale-free Networks

The study on dynamics of infectious diseases has important practical significance.This paper mainly consider the effect of consciousness on the spread of disease and categorizing the crowd,to make the model more reasonable.Firstly,Chapter 1 introduces the research significance and the research background of infectious disease model,then introduces our research contents of this paper.In Chapter 2,we built an SIR model with two infected groups on scale-free networks.where(?).By using the method of the next generation ma-trix,we get the basic reproduction R0 of this model,and concluded that when R0<1,the disease-free equilibrium is global asymptotic stability;When R0>1,there is a unique endemic equilibrium and the disease is sustainable;Then analysis and compare two immu-nization schemes on scale-free network;At last using the numerical analysis to verify our main conclusions.In Chapter 3,we built an SIR model with two susceptible groups and two infected groups on scale-free networks where(?),(?).Also,we get the basic reproduction R0 of this model by using the method of the next generation matrix,and concluded that when R0<1,the disease-free equilibrium is locally asymptotic stability;When R0>1,there is a unique endemic equilibrium and proof that is global asymptotic stability by using the method of constructing the Lyapunov function;Then analysis and compare two immunization schemes on scale-free network;At last using the numerical sim-ulations to verify our main conclusions.In Chapter 4,Summarize the main conclusion of this paper and investigate some ideas for future research.