Research On Mathematical Models Of The Prevention And Control For Citrus Huanglongbing

In recent years,citrus huanglongbing has gradually spread to more than 50 countries around the world.Re-search on dynamic models is an important method to analyze the transmission law of citrus huanglongbing.It can evaluate the effectiveness of prevention and control measures,and provide reliable theoretical reference and data basis to develop more effective and more economical prevention and control strategies for the future.Therefore,two kinds of the huanglongbing dynamic models are established in this paper,and the dynamic behaviors of the models are discussed.The main work of this thesis can be divided as follows:In the first chapter,the background,significance of the research and the communication mechanism of huanglongbing are introduced.And the relative research progress and some preliminary knowledges are given.In the second chapter,a dynamic model of huanglongbing with spreading in a grove is established,in which an impulsive control strategy of removing infected trees and dead trees is adopted and the general incidence is taken into consideration.By the method of fluctuation,the dynamic behaviors are analyzed.Theoretical results show that if R₁<1 the disease-free periodic solution is global attractive and the disease becomes extinct,if R₂>1,the disease-free periodic solution is unstable and the disease is uniformly per-sistent.By numerical simulation,the theoretical results are illustrated and sensitivity analysis is given.The simulation indicates that:?i?pulsing roguing infected citrus trees is an effective method for Huanglongbing control,?ii?increasing the replanting rate is bad for Huanglongbing control,?iii?increasing Huanglongbing induced death rate is benefit for Huanglongbing control.In the third chapter,according to the growth rhythm of citrus psyllid population with seasonal variation,citrus huanglongbing model with two measures is proposed,including killing psyllids and removing infected trees.First,the existence of disease-free periodic solution is proved.Then the basic reproductive number R₀is calculated.Finally,it is also proved that the basic reproduction number R₀ serves as a threshold value that determines whether the disease dies out or not.That is to say,if R₀<1,the disease-free periodic solution is globally asymptotically stable,whereas,if R₀>1,the disease-free periodic solution is not stable,disease is uniformly persistent.