Transmission dynamics and optimal control of stage-structured HLB model

Yunbo Tu; Shujing Gao; Yujiang Liu; Di Chen; Yan Xu; Yunbo Tu; Shujing Gao; Yujiang Liu; Di Chen; Yan Xu

doi:10.3934/mbe.2019259

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 5180-5205. doi: 10.3934/mbe.2019259

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Research article Special Issues

Transmission dynamics and optimal control of stage-structured HLB model

1.
Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou 341000, China
2.
National Research Center of Navel Orange Engineering and Technology, Gannan Normal University, Ganzhou 341000, China

Received: 25 March 2019 Accepted: 30 May 2019 Published: 06 June 2019

Citrus Huanglongbing (HLB) is one of severe quarantine diseases affecting citrus production both in abroad and domestic. Based on the mechanism and characteristics of citrus HLB transmission, we establish a vector-borne model with stage structure and integrated strategy and investigate the effect of the strategy in controlling the spread of HLB. By calculating, we obtain the basic reproductive number $R_0$, and prove that the disease can be eradicated if $R_0 < 1$, whereas the disease will persist if $R_0>1$. Meanwhile, we apply the optimal control theory to obtain an optimal integrated strategy. Finally, we use our model to simulate the data of the numbers of inspected and infected citrus trees in "Yuan Orchard", located in Ganzhou City, Jiangxi Province in the southeast of P.R China. We also give some numerical simulations for our theoretical findings.
- Huanglongbing,
- stage-structured model,
- basic reproductive number,
- population dynamics,
- optimal control
Citation: Yunbo Tu, Shujing Gao, Yujiang Liu, Di Chen, Yan Xu. Transmission dynamics and optimal control of stage-structured HLB model[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 5180-5205. doi: 10.3934/mbe.2019259

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Abstract

Citrus Huanglongbing (HLB) is one of severe quarantine diseases affecting citrus production both in abroad and domestic. Based on the mechanism and characteristics of citrus HLB transmission, we establish a vector-borne model with stage structure and integrated strategy and investigate the effect of the strategy in controlling the spread of HLB. By calculating, we obtain the basic reproductive number $R_0$, and prove that the disease can be eradicated if $R_0 < 1$, whereas the disease will persist if $R_0>1$. Meanwhile, we apply the optimal control theory to obtain an optimal integrated strategy. Finally, we use our model to simulate the data of the numbers of inspected and infected citrus trees in "Yuan Orchard", located in Ganzhou City, Jiangxi Province in the southeast of P.R China. We also give some numerical simulations for our theoretical findings.

References

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