Mirrored dynamics of a wild mosquito population suppression model with Ricker-type survival probability and time delay

Zhongcai Zhu; Xiaomei Feng; Xue He; Hongpeng Guo; Zhongcai Zhu; Xiaomei Feng; Xue He; Hongpeng Guo

doi:10.3934/mbe.2024083

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 2: 1884-1898. doi: 10.3934/mbe.2024083

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Mirrored dynamics of a wild mosquito population suppression model with Ricker-type survival probability and time delay

1.
Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
2.
College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
3.
College of Science, Xi'an University of Science and Technology, Xi'an 710054, China
4.
School of Mathematics and Informational Technology, Yuncheng University, Yuncheng 044000, China
5.
College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China

Academic Editor: Mingji Zhang

Received: 22 November 2023 Revised: 26 December 2023 Accepted: 29 December 2023 Published: 04 January 2024

Here, we formulated a delayed mosquito population suppression model including two switching sub-equations, in which we assumed that the growth of the wild mosquito population obeys the Ricker-type density-dependent survival function and the release period of sterile males equals the maturation period of wild mosquitoes. For the time-switched delay model, to tackle with the difficulties brought by the non-monotonicity of its growth term to its dynamical analysis, we employed an essential transformation, derived an auxiliary function and obtained some expected analytical results. Finally, we proved that under certain conditions, the number of periodic solutions and their global attractivities for the delay model mirror that of the corresponding delay-free model. The findings can boost a better understanding of the impact of the time delay on the creation/suppression of oscillations harbored by the mosquito population dynamics and enhance the success of real-world mosquito control programs.
- dengue fever,
- mosquito population suppression,
- sterile male mosquitoes,
- periodic solutions,
- Ricker-type survival probability
Citation: Zhongcai Zhu, Xiaomei Feng, Xue He, Hongpeng Guo. Mirrored dynamics of a wild mosquito population suppression model with Ricker-type survival probability and time delay[J]. Mathematical Biosciences and Engineering, 2024, 21(2): 1884-1898. doi: 10.3934/mbe.2024083

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Abstract

Here, we formulated a delayed mosquito population suppression model including two switching sub-equations, in which we assumed that the growth of the wild mosquito population obeys the Ricker-type density-dependent survival function and the release period of sterile males equals the maturation period of wild mosquitoes. For the time-switched delay model, to tackle with the difficulties brought by the non-monotonicity of its growth term to its dynamical analysis, we employed an essential transformation, derived an auxiliary function and obtained some expected analytical results. Finally, we proved that under certain conditions, the number of periodic solutions and their global attractivities for the delay model mirror that of the corresponding delay-free model. The findings can boost a better understanding of the impact of the time delay on the creation/suppression of oscillations harbored by the mosquito population dynamics and enhance the success of real-world mosquito control programs.

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