Modeling and analysis of release strategies of sterile mosquitoes incorporating stage and sex structure of wild ones

Mingzhan Huang; Xiaohuan Yu; Shouzong Liu; Mingzhan Huang; Xiaohuan Yu; Shouzong Liu

doi:10.3934/era.2023198

Electronic Research Archive

2023, Volume 31, Issue 7: 3895-3914. doi: 10.3934/era.2023198

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Research article

Modeling and analysis of release strategies of sterile mosquitoes incorporating stage and sex structure of wild ones

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

Received: 01 March 2023 Revised: 20 April 2023 Accepted: 04 May 2023 Published: 15 May 2023

This paper proposes and studies a switched interactive model of wild and sterile mosquitoes with stage and sex structure. Sterile males are released periodically and impulsively and remain sexually active for time $ \bar{T} $. We investigate the dynamical behavior of the system when the release period $ T $ is shorter than the sexual lifespan $ \bar{T} $, corresponding to a relatively frequent release. We first determine two important thresholds, $ m_1^* $ and $ m_2^* $, for the release amount $ m $ and prove the exponential asymptotic stability of the extinction equilibrium. Using fixed point theory, we establish the existence of positive periodic solutions for $ 0 < m < m_1^* $ and $ m_1^*\leq m < m_2^* $. Furthermore, by applying the comparison theorem of monotone systems, we demonstrate that the extinction equilibrium is globally asymptotically stable when $ m\geq m_2^* $. Finally, numerical examples are presented to confirm our theoretical results.
- switched system,
- extinction equilibrium,
- periodic solution,
- stability
Citation: Mingzhan Huang, Xiaohuan Yu, Shouzong Liu. Modeling and analysis of release strategies of sterile mosquitoes incorporating stage and sex structure of wild ones[J]. Electronic Research Archive, 2023, 31(7): 3895-3914. doi: 10.3934/era.2023198

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Abstract

This paper proposes and studies a switched interactive model of wild and sterile mosquitoes with stage and sex structure. Sterile males are released periodically and impulsively and remain sexually active for time $ \bar{T} $. We investigate the dynamical behavior of the system when the release period $ T $ is shorter than the sexual lifespan $ \bar{T} $, corresponding to a relatively frequent release. We first determine two important thresholds, $ m_1^* $ and $ m_2^* $, for the release amount $ m $ and prove the exponential asymptotic stability of the extinction equilibrium. Using fixed point theory, we establish the existence of positive periodic solutions for $ 0 < m < m_1^* $ and $ m_1^*\leq m < m_2^* $. Furthermore, by applying the comparison theorem of monotone systems, we demonstrate that the extinction equilibrium is globally asymptotically stable when $ m\geq m_2^* $. Finally, numerical examples are presented to confirm our theoretical results.

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