Dynamic Analysis Of Plant Disease Model With Discontinuous Control Strategy

In this paper,a class of Filippov plant diseases model with an economic threshold and a.class of Filippov plant diseases model with saturation incidence are investigated on the basis of classical infectious disease models.The global dynamical behaviors of the models are analy zed and discussed using the qualitative theory of differential equations,stability theory,and the differential equations with discontinuous righthand sides.The full paper is divided into four chapters.In Chapter 1,we introduce the background and significance of plant diseases model,the current status of domestic and international researches,and the main contents of this paper.In Chapter 2,we mainly introduce some preparatory knowledge,including Filippov system,Lyapunov method,Poincare map and so on.In Chapter 3,a plant disease model with an economic threshold is proposed,where the number of susceptible plants replanted depends on the number of infected plants removed.The global dynamics is investigated in depth using the Lyapunov method and the Poincarémap.We demonstrate the global asymptotic stability of disease-free equilibrium,endemic equilibrium and pseudo-equilibrium.In addition,results for finite time convergence of the number of diseased plants are given.The theoretical results obtained suggest that control objectives can be achieved by adopting appropriate removal and replanting rates.In Chapter 4,the effect of nonlinear incidence on the dynamics of plant diseases model is investigated,and a class of Filippov plant diseases model with saturated incidence is developed based on the classical infectious disease models.The global asymptotic stability of the equilibrium(disease-free equilibrium,endemic equilibrium and pseudo-equilibrium)of the model was obtained by Lyapunov’s method and LaSalle invariance principle.The obtained results indicate that appropriate adoption of control measures can control the number of infected plants below an economic threshold.At the end of the paper,the main research work of this paper is summarized and the main future research is anticipated.