Establishing <i>Wolbachia</i> in the wild mosquito population: The effects of wind and critical patch size

Yunfeng Liu; Guowei Sun; Lin Wang; Zhiming Guo; Yunfeng Liu; Guowei Sun; Lin Wang; Zhiming Guo

doi:10.3934/mbe.2019219

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 4399-4414. doi: 10.3934/mbe.2019219

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Establishing Wolbachia in the wild mosquito population: The effects of wind and critical patch size

1.
School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China
2.
School of Mathematics and Information Technology, Yuncheng University, Yuncheng, Shanxi, 044000, China
3.
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

Received: 27 February 2018 Accepted: 24 April 2019 Published: 20 May 2019

Releasing mosquitoes with Wolbachia into the wild mosquito population is becoming the very promising strategy to control mosquito-borne infections. To investigate the effects of wind and critical patch size on the Wolbachia establishment in the wild mosquito population, in this paper, we propose a diffusion-reaction-advection system in a heterogeneous environment. By studying the related eigenvalue problems, we derive various conditions under which Wolbachia can fully establish in the entire wild mosquito population. Our findings may provide some useful insights on designing practical releasing strategies to control the mosquito population.
- Wolbachia,
- advection,
- the minimal patch size,
- mosquito-borne,
- heterogeneous environment
Citation: Yunfeng Liu, Guowei Sun, Lin Wang, Zhiming Guo. Establishing Wolbachia in the wild mosquito population: The effects of wind and critical patch size[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4399-4414. doi: 10.3934/mbe.2019219

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Abstract

Releasing mosquitoes with Wolbachia into the wild mosquito population is becoming the very promising strategy to control mosquito-borne infections. To investigate the effects of wind and critical patch size on the Wolbachia establishment in the wild mosquito population, in this paper, we propose a diffusion-reaction-advection system in a heterogeneous environment. By studying the related eigenvalue problems, we derive various conditions under which Wolbachia can fully establish in the entire wild mosquito population. Our findings may provide some useful insights on designing practical releasing strategies to control the mosquito population.

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