Research ArticleNo Access

Dynamical behavior of a mosquito population suppression model composed of two sub-models

Mingzhan Huang

College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China

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Xiaohuan Yu

College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China

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Shouzong Liu

College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China

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, and

Xinyu Song

https://orcid.org/0000-0002-3861-1320

College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China

College of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, P. R. China

E-mail Address: xysong88@163.com

Corresponding author.

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https://doi.org/10.1142/S1793524522501261Cited by:3 (Source: Crossref)

Abstract

In this paper, a new mosquito population suppression model with stage and sex structure is constructed, which is composed of two sub-models switching each other. Sterile mosquitoes are released with period $T$ $T$ and remain sexually active for time $ˉ T$ $\bar{T}$ . For the case $ˉ T < T$ $\bar{T} < T$ , three thresholds $T^{*},$ $T^{*},$ $m^{*}$ $m^{*}$ and $c^{*}$ $c^{*}$ are determined for the release period $T$ $T$ and release amount $c$ $c$ . According to the values of $T$ $T$ and $c$ $c$ in different ranges determined by these thresholds, we study the dynamical behavior of the system for different release strategies, mainly including the existence and stability of the mosquito-extinction equilibrium and positive periodic solutions. Finally, some numerical simulations are performed to illustrate our results.

Keywords:

AMSC: 92D25, 92D40, 34C60

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