Oscillation threshold for a mosquito population suppression model with time delay

Yuanxian Hui; Genghong Lin; Qiwen Sun; Yuanxian Hui; Genghong Lin; Qiwen Sun

doi:10.3934/mbe.2019367

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 7362-7374. doi: 10.3934/mbe.2019367

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Oscillation threshold for a mosquito population suppression model with time delay

1.
Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, PRC
2.
School of Mathematics and Statistics, Pu’er University, Pu’er, 665000, PRC

Received: 07 May 2019 Accepted: 07 August 2019 Published: 09 August 2019

We consider a mosquito population suppression model with time delay. We show that, in the absence of sterile mosquitoes released, the model solutions oscillate with respect to its unique non-zero equilibrium. With the releases of sterile mosquitoes, we then determine an oscillation threshold, denoted by $\hat{b}$, for the constant release rate of the sterile mosquitoes such that all non-trivial positive solutions oscillate when the release rate of the sterile mosquitoes is less than $\hat{b}$, and the oscillation disappears as the release rate exceeds $\hat{b}$. We also provide some numerical simulations to validate our theoretical results.
- oscillation threshold,
- mosquito population suppression model,
- time delay,
- sterile mosquitoes
Citation: Yuanxian Hui, Genghong Lin, Qiwen Sun. Oscillation threshold for a mosquito population suppression model with time delay[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7362-7374. doi: 10.3934/mbe.2019367

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Abstract

We consider a mosquito population suppression model with time delay. We show that, in the absence of sterile mosquitoes released, the model solutions oscillate with respect to its unique non-zero equilibrium. With the releases of sterile mosquitoes, we then determine an oscillation threshold, denoted by $\hat{b}$, for the constant release rate of the sterile mosquitoes such that all non-trivial positive solutions oscillate when the release rate of the sterile mosquitoes is less than $\hat{b}$, and the oscillation disappears as the release rate exceeds $\hat{b}$. We also provide some numerical simulations to validate our theoretical results.

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