The effect of migration on transmission of <i>Wolbachia</i> in <i>Nilaparvata lugens</i>

Zhigang Liu; Tiejun Zhou; Zhigang Liu; Tiejun Zhou

doi:10.3934/mbe.2023895

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 11: 20213-20244. doi: 10.3934/mbe.2023895

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The effect of migration on transmission of Wolbachia in Nilaparvata lugens

Zhigang Liu ^1,2,3,
Tiejun Zhou ^{4
,
,}

1.
College of Plant Protection, Hunan Agricultural University, Changsha, 410128, Hunan, China
2.
College of Mathematics and Statistics, Hengyang Normal University, Hengyang, 421008, Hunan, China
3.
Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, Guangdong, China
4.
College of Information and Intelligence Science, Hunan Agricultural University, Changsha, 410128, Hunan, China

Academic Editor: Xiangsheng Wang

Received: 17 September 2023 Revised: 19 October 2023 Accepted: 24 October 2023 Published: 06 November 2023

Brown planthopper Nilaparvata lugens, which can transmit rice ragged stunt virus, is a serious and damaging pest to rice plants. Rice plants can protect themselves from the associated diseases of N.lugens by either suppressing or replacing N.lugens by releasing N.lugens infected by a special strain of Wolbachia wStri. The long-distance migration habit of N.lugens is one of the important precursors leading up to the large-scale occurrence of N.lugens. To study the effect of migration on the transmission of Wolbachia in N.lugens, a Wolbachia spreading dynamics model with migration of N.lugens between two patches is put forward. The existence and local stability conditions of equilibrium points of the system and its subsystems are obtained. Moreover, the effects of migration on the dynamic properties and the control of N.lugens are analyzed; the results show that the system can exhibit a bistable phenomenon, and the migration can change the stability of equilibrium infected with wStri from stable to unstable. The quantitative control methods for the migration of the insect N.lugens are proposed, which provide a theoretical guidance for future field experiments. Lastly, we use the Markov chain Monte Carlo (MCMC) method to estimate the parameters of the wild N.lugens migration model based on limited observational data; the numerical simulation results show that migration can increase the quantity of N.lugens, which is consistent with the relevant experimental results.
- Wolbachia,
- Nilaparvata lugens,
- Migration,
- stability,
- mathematical modeling
Citation: Zhigang Liu, Tiejun Zhou. The effect of migration on transmission of Wolbachia in Nilaparvata lugens[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 20213-20244. doi: 10.3934/mbe.2023895

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Abstract

Brown planthopper Nilaparvata lugens, which can transmit rice ragged stunt virus, is a serious and damaging pest to rice plants. Rice plants can protect themselves from the associated diseases of N.lugens by either suppressing or replacing N.lugens by releasing N.lugens infected by a special strain of Wolbachia wStri. The long-distance migration habit of N.lugens is one of the important precursors leading up to the large-scale occurrence of N.lugens. To study the effect of migration on the transmission of Wolbachia in N.lugens, a Wolbachia spreading dynamics model with migration of N.lugens between two patches is put forward. The existence and local stability conditions of equilibrium points of the system and its subsystems are obtained. Moreover, the effects of migration on the dynamic properties and the control of N.lugens are analyzed; the results show that the system can exhibit a bistable phenomenon, and the migration can change the stability of equilibrium infected with wStri from stable to unstable. The quantitative control methods for the migration of the insect N.lugens are proposed, which provide a theoretical guidance for future field experiments. Lastly, we use the Markov chain Monte Carlo (MCMC) method to estimate the parameters of the wild N.lugens migration model based on limited observational data; the numerical simulation results show that migration can increase the quantity of N.lugens, which is consistent with the relevant experimental results.

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