Study On Dynamical Models For Citrus Huanglongbing

Huanglongbing (HLB), a destructive disease of citrus and one of vector-borne disease, can betransmitted by citrus psyllid. Accordding to the characteristics of HLB transmission, we proposenon-autonomous HLB transmission models and an impulsive control model for HLB transmissionin this paper, and the dynamical properties of these models have been studied. What’s more, theaffection of HLB transmission on seasonal fluctuations and impulsive control has been discussed.The main contents of the paper are summarized as followings:In the first chapter, we introduce the purpose and significance of HLB, and also review thedomesic and the international research status of HLB at present. At the same time, we give themain work and the organization of this paper.In the second chapter, a transmission model of HLB which coefficients are periodic functionsis proposed. By the operator theory and the monodromy matrix theory, we obtain the basicreproduction number and demonstrate that the disease-free periodic solution is global stabilityforR01, whereas it is permanence forR01. Finally, we make numerical simulations tosupport our theoretical results and via sensitivity analysis we know that making an appropriatereduction of the recruitment rate of citrus are effective measures to control HLB.In the third chapter, a non-autonoumous model of HLB transmission has been studied. In thischarpter, we obtain the sufficient conditions for the extinction and permanence by contructing twoauxiliary functions. In final, we illustrate the validity of our result by numerical simulation.In the forth chapter, according the farmaers’ control strategy in the real world, we constructan impulsive control model for HLB transmission. The formulation of disease-free periodicsolution and the basic reproduction number of impulsive model is given. Finally, we prove that thedisease-free periodic solution is global stability forR01, and the disease permanent forR01.