Complex wolbachia infection dynamics in mosquitoes with imperfect maternal transmission

Bo Zheng; Wenliang Guo; Linchao Hu; Mugen Huang; Jianshe Yu; Bo Zheng; Wenliang Guo; Linchao Hu; Mugen Huang; Jianshe Yu

doi:10.3934/mbe.2018024

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 2: 523-541. doi: 10.3934/mbe.2018024

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Complex wolbachia infection dynamics in mosquitoes with imperfect maternal transmission

1.
College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510006, China
2.
Department of Parasitology of Zhongshan School of Medicine, Sun Yat-sen University, Guangzhou 510080, China
3.
Key laboratory for Tropical Diseases Control, (SYSU) Ministry of Education, Guangzhou, Guangdong 510080, China

Received: 27 December 2016 Accepted: 02 May 2017 Published: 01 April 2018
MSC : Primary: 92B05, 37N25; Secondary: 34D23, 92D30

Dengue, malaria, and Zika are dangerous diseases primarily transmitted by Aedes aegypti, Aedes albopictus, and Anopheles stephensi. In the last few years, a new disease control method, besides pesticide spraying to kill mosquitoes, has been developed by releasing mosquitoes carrying bacterium Wolbachia into the natural areas to infect the wild population of mosquitoes and block disease transmission. The bacterium is transmitted by infected mothers and the maternal transmission was assumed to be perfect in virtually all previous models. However, recent experiments on Aedes aegypti and Anopheles stephensi showed that the transmission can be imperfect. In this work, we develop a model to describe how the imperfect maternal transmission affects the dynamics of Wolbachia spread. We establish two useful identities and employ them to find sufficient and necessary conditions under which the system exhibits monomorphic, bistable, and polymorphic dynamics. These analytical results may help find a plausible explanation for the recent observation that the Wolbachia strain wMelPop failed to establish in the natural populations in Australia and Vietnam.
- Population dynamics,
- Wolbachia,
- imperfect maternal transmission,
- cytoplasmic incompatibility,
- monomorphism,
- polymorphism,
- bistability
Citation: Bo Zheng, Wenliang Guo, Linchao Hu, Mugen Huang, Jianshe Yu. Complex wolbachia infection dynamics in mosquitoes with imperfect maternal transmission[J]. Mathematical Biosciences and Engineering, 2018, 15(2): 523-541. doi: 10.3934/mbe.2018024

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Abstract

Dengue, malaria, and Zika are dangerous diseases primarily transmitted by Aedes aegypti, Aedes albopictus, and Anopheles stephensi. In the last few years, a new disease control method, besides pesticide spraying to kill mosquitoes, has been developed by releasing mosquitoes carrying bacterium Wolbachia into the natural areas to infect the wild population of mosquitoes and block disease transmission. The bacterium is transmitted by infected mothers and the maternal transmission was assumed to be perfect in virtually all previous models. However, recent experiments on Aedes aegypti and Anopheles stephensi showed that the transmission can be imperfect. In this work, we develop a model to describe how the imperfect maternal transmission affects the dynamics of Wolbachia spread. We establish two useful identities and employ them to find sufficient and necessary conditions under which the system exhibits monomorphic, bistable, and polymorphic dynamics. These analytical results may help find a plausible explanation for the recent observation that the Wolbachia strain wMelPop failed to establish in the natural populations in Australia and Vietnam.

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