Bifurcation analysis of a wild and sterile mosquito model

Xiaoli Wang; Junping Shi; Guohong Zhang; Xiaoli Wang; Junping Shi; Guohong Zhang

doi:10.3934/mbe.2019160

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 3215-3234. doi: 10.3934/mbe.2019160

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Research article

Bifurcation analysis of a wild and sterile mosquito model

1.
School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P.R.China
2.
Department of Mathematics, College of William and Mary, Williamsburg, Virginia, 23187-8795, USA

Received: 02 January 2019 Accepted: 31 March 2019 Published: 15 April 2019

The bifurcation of an ordinary differential equation model describing interaction of the wild and the released sterile mosquitoes is analyzed. It is shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, supercritical Hopf bifurcation, subcritical Hopf bifurcation, homoclinic bifurcation and Bogdanov-Takens bifurcation. We also find that the model displays monostable, bistable or tristable dynamics. This analysis suggests that the densities of the initial wild mosquitoes and the released sterile ones determine the asymptotic states of both populations. This study may give an insight into the estimation number of the released sterile mosquitoes.
- mosquitoes population model,
- tristable,
- hopf bifurcation,
- bogdanov-takens bifurcation,
- homoclinic bifurcation
Citation: Xiaoli Wang, Junping Shi, Guohong Zhang. Bifurcation analysis of a wild and sterile mosquito model[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3215-3234. doi: 10.3934/mbe.2019160

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Abstract

The bifurcation of an ordinary differential equation model describing interaction of the wild and the released sterile mosquitoes is analyzed. It is shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, supercritical Hopf bifurcation, subcritical Hopf bifurcation, homoclinic bifurcation and Bogdanov-Takens bifurcation. We also find that the model displays monostable, bistable or tristable dynamics. This analysis suggests that the densities of the initial wild mosquitoes and the released sterile ones determine the asymptotic states of both populations. This study may give an insight into the estimation number of the released sterile mosquitoes.

References

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