The Study On The Dynamical Behavior Of Several Plant Disease Models

Crop production is always subject to the constrains of plant diseases which can cause severelosses in economy. Therefore, agro-ecological sector, domestic and foreign experts, and farmersare very concerned about the issue of controlling plant diseases. Dynamic model and theory is oneof the most important method to study the spread of plant diseases. In this paper, based onprevious research, we study a nonautonomous plant disease model with latent period, a plantdisease model with cross protection, and a plant disease model with pulse rouging, and thedynamical properties of these models are studied.The main contents in this paper can be summarized as follows:In Chapter1, the purpose and significance of dynamic behavior of plant disease models areintroduced at first. Then, some research status and results recently about plant disease dynamicmodel are given. Finally, the main work and the organization of this paper are investigated.In Chapter2, a nonautonomous plant disease model with latent period is studied, thehorizontal transmission caused by insect vectors and vertical transmission through cuttingsreplanting are considered in our model. By constructing auxiliary functions, the dynamic behaviorof the model is studied, and the weaker integral form conditions for permanence and extinction ofdiseases are obtained. Finally, our theoretical results are confirmed by numerical simulation. Ourresults really improve the past results.In Chapter3, we discuss the effect of cross protection on virus control in plants, anonautonomous plant disease model with cross protection is formulated based on previous work.By using the comparison theory of differential system and the method of constructing multipleauxiliary functions, sufficient conditions for permanence and extinction of diseases are established.In addition, our main conclusions are confirmed by numerical simulation, at the same time, theeffectiveness of cross protection on virus control in plants is verified.In Chapter4, we investigate a non-autonomous plant diseases model with pulse rouging.By using Floquet theory and the comparison theorem of impulsive differential equations, weobtain the sufficient and necessary conditions of global asymptotical stability of the disease-freeperiodic solution and permanence of the system, and show thatR01is a threshold condition.Finally, the theoretical results are confirmed by numerical simulations, and the effects of pulseroguing on infected plants are studied.