Analysis Of An SIS Model On Dynamic Complex Networks

Infectious disease is one of the major factors threatening human health,it is of great significance to study the transmission mechanism and control its spreading.In this paper,we consider an SIS model with birth and death on complex networks,it has important theoretical and practical significance.In Chapter 1,we first introduce the research background and significance of epidemic,and then analysis the progress of epidemic dynamics on complex networks,finally give the main research content of this paper.In Chapter 2,we establish an SIS epidemic model on dynamic complex networks.We get the basic reproduction number R0 of the above model,and prove that when R0<1,the disease-free equilibrium is globally asymptotically stable.It can be seen from the numerical simulation,when R0<1 the disease-free equilibrium is globally attractive,and the disease gradually disappear;when R0>1,there exists a unique endemic equilibrium,and the disease is persistent.In Chapter 3,we consider the interaction between the two different kinds of contact modes,on dynamic complex networks we built an SIS epidemic model based on heterogeneous and random.By using the next generation matrix method,we get the basic reproduction number R0 of the above model,and get the globally property of the equilibrium.It can be seen from numerical simulation that the demographics has influences for the epidemic threshold.In Chapter 4,we summarizes the main conclusions of this paper and discusses some ideas for future research.