Global dynamics of a mosquito population suppression model with stage and sex structure

Junjie He; Di Li; Shouzong Liu; Junjie He; Di Li; Shouzong Liu

doi:10.3934/math.2023717

AIMS Mathematics

2023, Volume 8, Issue 6: 14027-14046. doi: 10.3934/math.2023717

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Research article

Global dynamics of a mosquito population suppression model with stage and sex structure

College of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, China

Received: 02 January 2023 Revised: 01 April 2023 Accepted: 04 April 2023 Published: 14 April 2023
MSC : 92B05, 92D25, 37N25

In this paper, we study a kind of mosquito population suppression model incorporating the growth stage as well as the sex structure of mosquitoes. For the general non-autonomous case, a threshold $ m^* $ for the number of sexually active sterile mosquitoes in the field is defined, and sufficient conditions for successful suppression and partial suppression of wild mosquito population are obtained. For the first special case when the release period of the sterile mosquito is equal to its sexual lifespan, we determined the initial population size under which the mosquito population can be suppressed finally for different release intensities. For the latter special case when sterile mosquitoes are released with a constant rate, we give a threshold $ u^* $ for the release rate, and investigate the dynamic behavior of the system based on this threshold. Finally, some numerical examples are presented to confirm the theoretical results.
- mosquito population suppression,
- sterile mosquitoes,
- release,
- extinction,
- stability
Citation: Junjie He, Di Li, Shouzong Liu. Global dynamics of a mosquito population suppression model with stage and sex structure[J]. AIMS Mathematics, 2023, 8(6): 14027-14046. doi: 10.3934/math.2023717

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Abstract

In this paper, we study a kind of mosquito population suppression model incorporating the growth stage as well as the sex structure of mosquitoes. For the general non-autonomous case, a threshold $ m^* $ for the number of sexually active sterile mosquitoes in the field is defined, and sufficient conditions for successful suppression and partial suppression of wild mosquito population are obtained. For the first special case when the release period of the sterile mosquito is equal to its sexual lifespan, we determined the initial population size under which the mosquito population can be suppressed finally for different release intensities. For the latter special case when sterile mosquitoes are released with a constant rate, we give a threshold $ u^* $ for the release rate, and investigate the dynamic behavior of the system based on this threshold. Finally, some numerical examples are presented to confirm the theoretical results.

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