Research On Infectious Disease Model Based On Collective Population Network

Complex networks is an important model to simulate human social activity and the network system of the nature.The structure characteristics of complex networks determines that it can reflect the multiple link of each other between the individual,and the complex relationship of crisscrossing.There are a large number of complex systems in nature.we can create a variety of complex network model to describe them.Among them,the spread of infectious diseases system exactly corresponds with the structure characteristics of complex networks.The development of the infectious diseases dynamics in complex networks have been able to predict the law of the spread of infectious diseases more accurately.However,in the face of the complexity of the structure of the network system,the scholars still need to to research and research continuously.In the chapter 1,it introduces the nearby development of the modern dynamics of infectious diseases.With the development of complex network,the character of dynamic in the complex networks are found and explored by the experts and scholars.It gives a new hot spot to infectious disease dynamics research.It analyzes the research domestic and trends at home and abroad.It puts forward the important basic theory of research network structure,network model and the dynamic model of infectious diseases and other.In the chapter 2,We introduced the model of reaction diffusion process in general and established the corresponding mathematical model.Later,in based on the dynamic model of complex networks,we established the infectious disease model.We analyzed the stability of the disease-free equilibrium and the positive equilibrium point.In the chapter 3,First of all,we illustrate the important influences of saturation incidence in the process of the spread of infectious diseases.It states the actual infection in the process of spreading the overall trend.And it create a compositeparameters instead of the incidence of general,and by adding saturated incidence in general complex network of the incidence of infectious disease model to simulate the process of transmission of infectious diseases under saturated incidence rate.It makes use of the related theory of the infectious disease dynamics,the mathematical modeling of complex networks and differential equation qualitative and stability and other.It establish the dynamics model of the spread of the infectious disease on complex networks.It carries and analyses the stability of system and the existence of balance.And it makes numerical simulation.