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Oscillation threshold for a mosquito population suppression model with time delay

  • 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.

    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

    Related Papers:

  • 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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