The Study Of Epidemic Model With Nonlinear Incidence Rate

Exploring epidemic spreading and predicting its development trend are important aspects for epidemic study,and they are the basis of control policy adopted by the government and medical department.The aim of this work is to construct several mathematical models in epidemiology and to analyze the asymptotic behavior of these models.The full text is divided into five chapters:The first chapter introduced the study of infectious diseases and some methods about epidemiological models.The second chapter introduced some theoretical knowledge.The third chapter not only establish but also analyze a nonlinear high dimensional autonomous differential system SEIQR model in epidemiology.That the nonlinear incidence rate is used in the model,has included the traditional bilinear incidence rate.By analyzing global behavior of the model,we get a incisive comprehension about the disease propagation law and the disease extinction is determined by the basic reproduction number R₀.It showed that incresing isolation and improving the cure rate of the disease can control the spread of diaease;An SEIS epidemic model with constant input and nonlinear incidence rate is maily studied in the fourth chapter.The disease-free equilibrium is globally asymptotical stable by the means of Lasalle's invariant set theorem,Liapunov function and Hurwitze criterion.Using second additive compound matrix,it is proved that the unique endemic equilibrium is globally asymptotical stable.The results in this chapter suggest that giving the patients timely treatment and improving the cure rate are an effective way to control the disease.A kind of SEIS model infections in both latent and infected period is studied in the fifth chapter. The global analysis of this model becomes more complex.Through mathematical studied and simulation we find that giving the patients timely treatment,improving the cure efficiency and decreasing the infective coefficient are effective methods for the control of the disease.