Research On The Global Dynamics Of Multigroup SEIR Epidemic Models

Due to the worldwide spread of COVID-19,prevention and control of the epidemic disease and the prediction of its future development have become the focus of scholars.The SIR compartmental model^[26]created by Kermack and Mckendrick in 1926 is the basis of the epidemiological model.With the further development of epidemic models,people will consider the incubation period of the disease,and heterogeneity between infected persons due to different ages or regions when constructing the models.The dynamics of disease models have become the essential ingredient of the biomathematical models,can be used as an important theoretical basis for predicting disease development trends and optimizing disease prevention and control policies.In the thesis,we constructe multigroup SEIR epidemic model which is based on the practical significance that heterogeneity in host population can be the result of many factors.Additionally considere vaccination and mobility of the total population which would have an impact on the spread of the disease when constructing the models.In the first chapter,we introduce the background of the epidemic dynamics,the current research and development of multigroup SEIR models,the graph theory^[11].In the second chapter,two epidemic models are described,SIR model^[26]and multigroup SEIR model^[12].And the current research development of these models are introduced.In the third chapter,we construct the multigroup SEIR epidemc model:The basic reproduction number R₀ is calculated by the use of the next generation matrix^[6]and it is proved that when the basic reproduction number R₀< 1,the existence of diseasefree equilibrium and the local asymptotic stability are maintained in the system,and the disease would gradually disappear with time.And then,by using graph theory to construct an appropriate Lyapunov function,we prove that when the basic reproduction number R₀> 1,there is an endemic equilibrium in the system,and it is globally asymptotically stable in the feasible region.The disease will always exist in the population.In conclusion,the global dynamics of this model is completely determined by the basic reproduction number R₀.