### Mathematical Biosciences and Engineering

2019, Issue 5: 5180-5205. doi: 10.3934/mbe.2019259
Research article Special Issues

# Transmission dynamics and optimal control of stage-structured HLB model

• 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.

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

### Related Papers:

• 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.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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