Dynamical analysis of discrete models for mosquito population suppression

Ruibin Jiang; Zhiming Guo; Ruiqiang Zhuo; Ruibin Jiang; Zhiming Guo; Ruiqiang Zhuo

doi:10.3934/era.2025332

Electronic Research Archive

2025, Volume 33, Issue 12: 7528-7550. doi: 10.3934/era.2025332

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Dynamical analysis of discrete models for mosquito population suppression

School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

Received: 16 October 2025 Revised: 04 December 2025 Accepted: 09 December 2025 Published: 16 December 2025

Amid the global challenge of mosquito-borne disease transmission, sterile insect technology (SIT) has emerged as a promising biological control strategy. Based on the classical Beverton–Holt model and the assumption of complete cytoplasmic incompatibility (CI), we develop a discrete-time model with overlapping generations and a corresponding integro-difference equation (IDE) to investigate the population dynamics under different release strategies for infected male mosquitoes. For the discrete-time model, we apply stability and bifurcation theory to determine the existence and stability of equilibria and derive the release threshold $ r^* $ above which the wild mosquito population is successfully suppressed. Analysis of the IDE model yields a lower release threshold $ r^{**} $ and a critical patch-size $ L^* $. Comparison of the two models demonstrates that spatial diffusion reduces the required release threshold for achieving population suppression.
- stability,
- bifurcation,
- integro-difference equation,
- traveling wave,
- critical patch-size
Citation: Ruibin Jiang, Zhiming Guo, Ruiqiang Zhuo. Dynamical analysis of discrete models for mosquito population suppression[J]. Electronic Research Archive, 2025, 33(12): 7528-7550. doi: 10.3934/era.2025332

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Abstract

Amid the global challenge of mosquito-borne disease transmission, sterile insect technology (SIT) has emerged as a promising biological control strategy. Based on the classical Beverton–Holt model and the assumption of complete cytoplasmic incompatibility (CI), we develop a discrete-time model with overlapping generations and a corresponding integro-difference equation (IDE) to investigate the population dynamics under different release strategies for infected male mosquitoes. For the discrete-time model, we apply stability and bifurcation theory to determine the existence and stability of equilibria and derive the release threshold $ r^* $ above which the wild mosquito population is successfully suppressed. Analysis of the IDE model yields a lower release threshold $ r^{**} $ and a critical patch-size $ L^* $. Comparison of the two models demonstrates that spatial diffusion reduces the required release threshold for achieving population suppression.

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