The Analysis Of Epidemic Model Under The Network Environment

The epidemic has always existed with the development of human society.In recorded activities, the human survival has been subject to a variety of epidemics test. Epidemic propagation model using mathematical methods established can simulate a variety of characteristics of the spread of disease.Recently,more and more literatures on complex networks have been published,and the properties in the real world complex networks have been widely used. The real complex networks,scale-free feature and small world phenomenon has great influence on the spread of the disease, Because of this,studying the epidemic spread by the tools of complex networks become important practical significance. The preliminary research mainly dynamics a model under the network environment to the epidemic. The research content is mainly manifested as follows:1. We have a brief review of epidemic background,and we summarize the related knowledge points of epidemic and the history of epidemic, at the end we discussed the current research status of the epidemic.2.We construct a SIQRS epidemic model with saturated contact rate. Through the analysis of the model to prove the existence of the equilibrium, then use the related knowledge to prove the stability of equilibrium.By the numerical simulation, we get the image of the theoretical analysis, which means the analysis above is right.3.Based on the traditional model SIR, we establish a new form of SIR epidemic model. Found the spread of the epidemic threshold. Then in the case of the corresponding lower.We analyze the stability of the equilibrium point of the epidemic.4.It summarizes the main work done in the paper and prospect the development of complex networks.