Research On Dynamics Models Of A Few Kinds Of Citrus Huanglongbing

Huanglongbing cause devastating damage to citrus industry.Dynamic models are conducive to study disease transmission rule,and evaluate the effect of disease prevention.In order to assess the effect of control measures on huanglongbing spread rule,such as seasonal fluctuations,cross protection,tree removal and so on,we establish a high dimensional autonomous citrus huanglongbing disease dynamics model.Specific contents are summarized as follows:In the first chapter,we introduced briefly research background and current situation of citrus huanglongbing,bifurcation and switched system.Finally,we put forward the research content and structure of this thesis.In the second chapter,in order to study the transmission of huanglongbing in the south of Jiangxi,we formulated huanglongbing dynamic model with cross protection and mixed planting.The basic reproductive numbers of two models,R₀,were defined and calculated.The locally asymptotical stability of the disease-free equilibrium and the permanence of two models are proved.Sufficient conditions of existence of backward bifurcation were gained.The theoretical research results showed thatR₀?27?1 is no longer sufficient for disease elimination.The numerical simulation illustrated the theoretical results.In the third chapter,by introducing switching parameters into a general impulsive huanglongbing model,we constructed a novel impulsive switching model for huanglongbing with seasonal fluctuations.Firstly,we theoretically investigated the basic reproductive number and its computation formulae of the model,and proved the permanence of the model.Finally,the numerical simulation imply that spring and autumn are the optimum seasons for killing psyllids,and winter is the optimum season for removing infected trees.