Research On Time Delayed Dynamic Models And The Control For Citrus Huanglongbing

Huanglongbing?HLB?,known as the cancer of citrus,has spread widely in many countries around the world.It is mainly transmitted by insect vector,citrus psyllid,and has devastating effects on the development of citrus industry.In the south of China,the epidemic in citrus-growing areas is accelerating and aggravating,which not only affects the safety of citrus production,but also has a negative impact on orange farmers and export trade.Hence,the prevention and control of HLB has become an important issue.In recent decades,applying mathematical models to study the propagation dynamics of HLB has been regarded an effective means to prevent and control HLB.In this thesis,delayed models and switching models for HLB are pre-sented and studied.The threshold values and dynamic behaviors for these models are studied.And the main work of this thesis is summarized as follows.In the first chapter,the background and significance of research of HLB were introduced.And then the research status of epidemic dynamics model were shown briefly.Finally,we present some useful results related to this article.In the second chapter,we proposed a delay model for HLB with latent period and calculated the basic reproductive number R₀.Further,we verified that disease-free equilibrium of the system is globally asymp-totically stable if R₀<1;Whereas there is a unique endemic equilibrium if R₀>1.Finally,we obtained sufficient conditions for locally asymptotically stable positive equilibrium and existence of Hopf bifurca-tion.In the third chapter,a time-delayed HLB model with a novel type of incidence rate is presented.Firstly,the basic reproductive number for this model is given,and it is proved that the disease will die out when R₀<1,and persists if R₀>1.Further,A set of sufficient conditions for the global attractivity of the endemic equilibrium by the method of fluctuations are established.Numerical simulations are carried out to illustrate the effectiveness of the obtained result.In the last chapter,we presented two switching HLB models with continuous and impulsive control strategies.At first,by taking into account of the variable parameters,including transmission rate,killing rate and removing rate,we proposed a new switching HLB model with continuous control,and derive a threshold value that measures the persistence of the disease.Furthermore,pulse control is applied to the continuous HLB model and some novel threshold conditions are established to ensure the existence and stability of the periodic disease-free solution.Numerical simulations are carried out to illustrate the effectiveness of the obtained result.