Dynamic Modeling Of The Transmission And Control In Citrus Huanglongbing

Citrus Huanglongbing（HLB）is a devastating disease of citrus caused by Candidatus Liberibacter asiaticus.HLB is mainly transmitted by the vector citrus psyllid and is the most destructive citrus disease worldwide.The disease has infected citrus-growing areas in nearly 50 countries and territories,posing an unprecedented challenge to the global agricultural economy and health.The epidemic situation in citrus production areas in China is serious,which not only affects the development of the citrus industry in China but also has a negative impact on fruit farmers’poverty alleviation,income increase,and rural revitalization.Therefore,the integrated control of citrus HLB has become an important issue.Using mathematical models to investigate the transmission dynamics of HLB has become one of the effective means to prevent and control the spread of this disease in recent years.Based on the biological background of HLB,this paper proposes research questions,establishes a corresponding mathematical model,studies the dynamic properties of the model,and gives some theoretical results that are difficult to obtain in experiments.The main contents of this dissertation include the following aspects:（1）A deterministic dynamical model is proposed to explore the transmission dy-namics of HLB between citrus tree and Asian citrus psyllid（ACP）.Using the theory of dynamical system,the dynamics of the model are rigorously analyzed.The results show that the disease-free equilibrium is globally asymptotically stable when the basic repro-duction number R₀<1,and when R₀>1 the system is uniformly persistent.Applying the global sensitivity analysis of R₀,some parameters that have the greatest impact on HLB transmission dynamics are obtained.Furthermore,the optimal control theory is applied to the model to study the corresponding optimal control problem.Both analyt-ical and numerical results show that:（i）the infected ACP plays a decisive role in the transmission of HLB in citrus trees,and eliminating the ACP will be helpful to curtail the spread of HLB;（ii）optimal control strategy is superior to the constant control strategy in decreasing the prevalence of the diseased citrus trees,and the cost of implementing op-timal control is much lower than that of the constant control strategy;and（iii）spraying insecticides is more effective than other control strategies in reducing the number of ACP in the early phase of the transmission of HLB.These theoretical and numerical results may be helpful in making public policies to control HLB in orchards more effectively.（2）To evaluate and compare the superiority and cost-effectiveness of various control strategies for HLB,a mathematical model of stage structure of citrus psyllid vector is es-tablished.Based on strict mathematical derivations,the explicit expression for the basic reproduction number（R₀）of HLB is derived.The dynamics of the model are rigorously analyzed by using the theory of dynamical system.The theoretical results show that the disease-free equilibrium is globally asymptotically stable if R₀<1,and if R₀>1 the system is uniformly persistent.By applying the global sensitivity analysis of R₀,we can obtain some parameters with the most significant influence on the transmission dynamics of HLB.Moreover,the optimal control theory is used to investigate the corresponding optimal control problem of the epidemic model.Numerical simulations are conducted to reinforce the analytical results.Using the cost-effectiveness analysis,the superiority of various intervention strategies is compared by calculating Incremental Cost-Effectiveness Ratio（ICER）value.The findings imply that coupled control strategy involving insecti-cide spraying treatment and HLB-symptomatic trees removal is the most cost-effective strategy and belongs to long-term intervention measures,and it is recommended to take this strategy to control the disease in the whole process.On the contrary,nutrient so-lution treatment and yellow sticky trap control are short-term intervention measures,which can be used at the initial stage of disease outbreak but discontinued at the later stage due to cost considerations.（3）To understand the impact of sexual transmission on HLB dynamics,we propose a host-vector-HLB compartment model incorporating two transmission routes.The basic reproduction number R₀is derived.Various interventions of the disease are assessed.We also investigate the effect of different incidence functions to simulate sexual transmis-sion.For the case of sublinear incidence functions,the disease-free equilibrium is globally asymptotically stable（GAS）provided R₀<1.For mass action incidence of sexual trans-mission,the endemic equilibrium is GAS provided R₀>1.However,under nonlinear incidence,it is proved that the model may exhibit backward bifurcation.The theoretical and numerical studies reveal that:（i）different forces of infection between heterosexual psyllid in the model may have a distinct impact on disease dynamics;（ii）sensitivity anal-ysis shows that for R₀,the transmission rate between host and vector is more sensitive parameter than that between heterosexual psyllid;（iii）if the sexual transmission ignored,the disease burden is likely to be underestimated in comparison with realistic scenarios;（iv）in the absence of chemical insecticides,the combined use of yellow sticky traps and injection of nutrient solutions can be more effective in suppressing the spread of HLB.（4）Planting disease-free citrus seedlings is one of the significant intervention strate-gies for HLB.In this paper,a compartment model is used to investigate the importation and local transmission of the disease.Due to the continuous input of the diseased cit-rus seedlings from outside,the traditional theoretical analysis methods are insufficient to describe and predict its dynamical behaviors based on the analysis determined by the basic reproductive ratio R₀.Then a complete theoretical,bifurcation,and sensitivity analysis are carried out on the simplified system.Based on our study,we have the fol-lowing interesting findings:（i）the importation of diseased citrus seedlings in orchards plays a vital role in the transmission of HLB,and planting disease-free citrus seedlings will effectively inhibit the spread of the disease;（ii）the importation of diseased citrus seedlings can affect the stability of the equilibrium of the full system;（iii）the simplified system may exhibit some complex dynamic phenomena,such as saddle-node bifurcation,forward bifurcation,backward bifurcation,and bistability;（iv）global sensitivity analysis shows that the mortality and biting rate of citrus psyllids have a greater impact on R₀than other parameters.