Analysis and control of Aedes Aegypti mosquitoes using sterile-insect techniques with Wolbachia

Rajivganthi Chinnathambi; Fathalla A. Rihan; Rajivganthi Chinnathambi; Fathalla A. Rihan

doi:10.3934/mbe.2022520

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 11154-11171. doi: 10.3934/mbe.2022520

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Analysis and control of Aedes Aegypti mosquitoes using sterile-insect techniques with Wolbachia

Rajivganthi Chinnathambi ^{1
,
,},
Fathalla A. Rihan ^{2
,
,}

1.
Division of Mathematics, School of Advances Sciences, Vellore Institute of Technology, Chennai, Tamilnadu-600 127, India
2.
Department of Mathematical Sciences, College of Science, United Arab Emirats University, Al-Ain 15551, UAE

Academic Editor: Wenrui Hao

Received: 26 May 2022 Revised: 22 July 2022 Accepted: 25 July 2022 Published: 04 August 2022

Combining Sterile and Incompatible Insect techniques can significantly reduce mosquito populations and prevent the transmission of diseases between insects and humans. This paper describes impulsive differential equations for the control of a mosquito with Wolbachia. Several interesting conditions are created when sterile male mosquitoes are released impulsively, ensuring both open- and closed-loop control. To determine the wild mosquito population size in real-time, we propose an open-loop control system, which uses impulsive and constant releases of sterile male mosquitoes. A closed-loop control scheme is also being investigated, which specifies the release of sterile mosquitoes according to the size of the wild mosquito population. To eliminate or reduce a mosquito population below a certain threshold, the Sterile insect technique involves mass releases of sterile insects. Numerical simulations verify the theoretical results.
- Aedes Aegypti mosquitoes,
- feedback control,
- stability,
- sterile insect technique,
- Wolbachia
Citation: Rajivganthi Chinnathambi, Fathalla A. Rihan. Analysis and control of Aedes Aegypti mosquitoes using sterile-insect techniques with Wolbachia[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11154-11171. doi: 10.3934/mbe.2022520

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Abstract

Combining Sterile and Incompatible Insect techniques can significantly reduce mosquito populations and prevent the transmission of diseases between insects and humans. This paper describes impulsive differential equations for the control of a mosquito with Wolbachia. Several interesting conditions are created when sterile male mosquitoes are released impulsively, ensuring both open- and closed-loop control. To determine the wild mosquito population size in real-time, we propose an open-loop control system, which uses impulsive and constant releases of sterile male mosquitoes. A closed-loop control scheme is also being investigated, which specifies the release of sterile mosquitoes according to the size of the wild mosquito population. To eliminate or reduce a mosquito population below a certain threshold, the Sterile insect technique involves mass releases of sterile insects. Numerical simulations verify the theoretical results.

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