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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

Special Issues: Inverse problems in the natural and social sciences

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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Keywords 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. Mathematical Biosciences and Engineering, 2019, 16(6): 7362-7374. doi: 10.3934/mbe.2019367

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