Dynamics Analysis Of Plant Epidemic Model

This paper mainly studies the dynamics of three kinds of plant disease models.The first part is the ordinary differential equation model,the second part is the delay differential equation model,and the last part is a plant-herbivore plant infectious disease model.In the first chapter,the research background,significance,research process and development trend of the infectious disease model are introduced,and the main contents of this study are summarized.In the second chapter,some of the preliminary knowledge used in this article is introduced.In the third chapter,the differential model is studied for a class of plant disease,the threshold which determines the outcome of the disease is given.Using the Lyapunov function,Routh-Hurwitz criteria and geometric method,the local and global asymptotic stability of the disease-free equilibrium and the positive equilibrium is obtained.In the fourth chapter,the stability and Hopf bifurcation of a class of plant epidemic model with time delay is investigated.The global stability of the disease-free equilibrium and the local stability of the positive equilibrium is analyzed.The center manifold theorem and the normal form theory is used to determine the stability of bifurcating periodic solutions and the direction of bifurcation.Numerical simulations is given to verify the existence of Hopf bifurcation.In the fifth chapter,a plant infectious disease model of plant-herbivores is studied.The number of equilibria is discussed,and the local stability of each equilibrium is analyzed.In the sixth chapter,we summarize the main research results of this thesis,and propose some problems that need to be solved.