Study On A Epidemic Dynamic Model With Nonlinear Incidence Rate

To prevent and control infectious diseases is an important problem for national economy and the people's livelihood,and it is the important basis to study the prevalent rule of diseases.epidemical dynamics founds the mathematical models which can reflect its rule of change on the basis of things such as outbreak, development and environment change of diseases, and it reveals developmental course of diseases by studying character of models, forcasts its prevalent Rule and developmental trend,analyses the reason and key factors of diseases,quests for the optimal strategies to prevent and control infectious diseases and provides theoretical and quantitative basis for the decision-making.In this paper,we study two kind epidemic dynamic model.First, we introduced a nonlinearity SIR mathematic model with constant importing but no Quarantine Kind.We Solve The model balancing point and given the model threshold value out a theorem.the existences and global approximation stabilities of the disease-free equilibrium and endemic equilibrium are solved.Then we studied a SIQS model with nonlinearity saturated contact rate, we has given the model balance point,the existences and global approximation stabilities of the disease-free equilibrium and endemic equilibrium are solved.but in this model,we Add in the Quarantine Kind,so Significance of the results obtained.This two ones adopt the Matlab software to have carried out the numerical value simulation, combine theoretical analysis, can make us ascertain those affecting factors to result, this is also a important purpose of builds a epidemic model...