Dynamic Behavior Analysis For The Transmission Model Of Avian Influenza

The emergence of new infectious diseases is increasingly threatening human health.According to statistics,more than half of new infectious diseases are zoonoses.Avian influenza,a zoonotic disease,has a high pathogenicity,which not only seriously affects the poultry industry,but also poses a threat to human health.Therefore,it is of great theoretical and practical significance to study the transmission law and control strategy of avian influenza infectious diseases.By analyzing the transmission background of avian influenza and considering more comprehensive infectious factors,an infectious disease model which is more in line with the law of disease transmission is established in this thesis.The stability of the new model was analyzed to provide theoretical basis for the prevention and control of avian influenza infectious diseases.The main contents of this paper are as follows:In Chapter 1,the research background and current situation of avian influenza transmission model are elaborated,and the research value and significance are given.In Chapter 2,the main preparatory knowledge needed for the research of this paper is given,including some related concepts,stability theory and research methods.In Chapter 3,taking H7N9 avian influenza as an example,according to the latency of its transmission,the dissemination of a class of human-avian interaction H7N9 avian influenza virus was studied,and the corresponding dynamics model was established.By using Lyapunov stability method,LaSalle invariant set principle and Li-Muldowney geometry method,the global stability of the model is discussed.It is concluded that the disease-free equilibrium of the model is globally asymptotically stable when the basic reproduction number is less than 1 and the endemic equilibrium of the model is globally asymptotically stable when the basic reproduction number is greater than 1.In Chapter 4,on the basis of Chapter 3,the H7N9 avian influenza epidemic model with mutant virus is further discussed,and its global behavior is analyzed.We obtain a new method to determine the global stability.By using this method,the global asymptotic stability conditions of the disease-free equilibrium and the endemic equilibrium of the new model are given.Furthermore,we partially solved the publicity problem raised by Iwami-Takeuchi-Liu.In Chapter 5,on the basis of Chapter 3,the influence of periodic environment on disease transmission is considered,and a SI-SEIR avian influenza model with latent effect is established in periodic environment,and the existence of periodic solution is analyzed.In Chapter 6,we summarized the main results of H7N9 avian influenza model,and put forward some problems that need further study.