Stability Analysis On A Class Of Epidemic Dynamic Model With Isolated Items And Vaccination

With the rapid development of world science and technology,health care,human beings in the process of fighting the diseases has made fruitful achievements.However,some of the emerging infectious diseases also deprived many precious lives mercilessly.It is very necessary to build the reasonable dynamic model of infectious diseases to find the more scientific effective reason for finding the best way to control infectious disease development.In this paper,on the basis of previous studies infectious disease model,build two kinds of infectious disease dynamics model with the isolated items and vaccination,and discuss its stability.Firstly,this paper introduces the meaning and current situation of infectious disease model development,also gives the basic concept,theorem,lemma concerning this paper,and puts forward the main content of this paper.Secondly,this paper build and analyze the SIQR model with isolated items and vaccination,by the relevant knowledge of differential equation,using the Liapunov function and Liapunov-Lasalle method to discuss the stability of the equilibrium,judge whether disease epidemic threshold value,put forward the strategy to control the disease according to the threshold value.Our theoretical results are confirmed by numerical simulations.Thirdly,we study SEIQR epidemical models with continuous and pulse vaccination,discuss the existence and stability of the infection-free periodic solution,and compares the threshold value in each vaccination situation,get more accurate and feasible vaccination strategies.At last,we summarize the conclusion of the thesis and propose unresolved issues of it,which needed to do further research and exploration in the future.