Dynamic Analysis Of Several Models Of Infectious Diseases With Incubation Periods In Livestock And Human Populations

In recent years,more than 70%of new infectious diseases are zoonotic diseases.The spread and control of zoonotic diseases has been the focus of attention of all walks of society.Three infectious disease models are established according to the transmission characteristics of zoonotic diseases and the impact of different control measures.In this paper,we mainly analyzed the three infections systems and obtained the local and global asymptotic stability of the equilibrium point.The correctness of some conclusions is verified by numerical simulation of MAT LAB.In chapter one.this paper mainly introduces the research status,development trends of infectious disease models and the necessary preparatory knowledge in this paper.In chapter two,we considered that human was infected through contact with infected humans:infected small ruminant,livestock,infected cattle and environment Brucella.we established the infectious disease model of livestock of an incubation period that spreading among the same.population.Firstly,we calculated the basic reproduction number R0 by the spectrum radius of the next-generation matrix.Secondly,we proved the global asymptotic stability of the disease-free equilibrium point and the endemic equilibrium point of the model by constructing the Lyapunov function and the Lasalle invariant principle.Finally correctness of some conclusions is verified by numerical simulation of MAT LAB.In chapter three,we established a,zoonotic infectious disease model with time delay by considering that the infected human have a period of time between initial infection and infectious.By studying the dynamic behavior of the time delay model,we calculated the basic production number R0 and proved the local and global asymptotic stability of the two equilibrium points of the model.Further,the corresponding the optimal control problem is formulated by introducing the control variables that namely slaughter intensity,immune injection rate and education effect.We obtained the optimal control pair by constructing the Hamiltonian function and the maximum criterion of the pontryagin with time delay.The correctness of some conclusions is verified by numerical simulations of MATLAB.In chapter four,on the basis of Chapter four,we considered the influence of media information,media information not only affect people's behavior and reduce the infection rate of human but also increase the slaughter intensity of infected livestock.In order to further optimized the model,we established the infectious disease model with media information effects and time delay.Firstly,we calculated the basic reproduction number R0 by the spectrum radius of the next-generation matrix,the equilibrium point and positive invariant set.Secondly,through constructing Lyapunov function and applying the Las all e invariant,set principle,the global asymptotic stability of the disease-free equilibrium point and the endemic equilibrium point of the model is proved.Finally,correctness of some conclusions is verified by numerical simulation of MAT LAB.In chapter five,we mainly summarizes the content of the full text,and proposes deficiencies and future research directions.