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Updated: Oct 3, 2025
Maintaining Aedes aegypti Mosquitoes Infected with Wolbachia
Published on: August 14, 2017
Uniqueness and stability of periodic solutions for an interactive wild and Wolbachia-infected male mosquito model
1College of Mathematics and Information Sciences, Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou, People's Republic of China.
Abstract:
We investigate a mosquito population suppression model, which includes the release of Wolbachia-infected males causing incomplete cytoplasmic incompatibility (CI). The model consists of two sub-equations by considering the density-dependent birth rate of wild mosquitoes. By assuming the release waiting period T is larger than the sexual lifespan of Wolbachia-infected males, we derive four thresholds: the CI intensity threshold , the release amount thresholds and , and the waiting period threshold . From a biological view, we assume throughout the paper. When , we prove the origin is locally asymptotically stable iff , and the model admits a unique T-periodic solution iff , which is globally asymptotically stable. When , we show the origin is globally asymptotically stable iff , and the model has a unique T-periodic solution iff , which is globally asymptotically stable. Our theoretical results are confirmed by numerical simulations.
Insights
We developed a mosquito population suppression model using Wolbachia-infected males with incomplete cytoplasmic incompatibility (CI). Our findings reveal critical thresholds for CI intensity and male release strategies to effectively control mosquito populations.
Area of Science:
- Mathematical Biology
- Vector Control
- Population Dynamics
Background:
- Mosquito-borne diseases pose significant public health challenges.
- Population suppression strategies are crucial for disease prevention.
- Wolbachia-based methods offer a novel approach to vector control.
Purpose of the Study:
- To investigate a mathematical model for mosquito population suppression.
- To analyze the impact of releasing Wolbachia-infected males with incomplete cytoplasmic incompatibility (CI).
- To determine critical thresholds for effective population control.
Main Methods:
- Developed a two-equation mathematical model incorporating density-dependent birth rates.
- Analyzed model stability and periodicity under varying parameters.
- Derived thresholds for CI intensity, release amounts, and waiting periods.
- Utilized theoretical analysis and numerical simulations.
Main Results:
- Identified four key thresholds: CI intensity, two release amounts, and waiting period.
- Established conditions for the stability of the origin (extinction) and the existence of a unique T-periodic solution (population persistence).
- Demonstrated that specific threshold conditions guarantee either global asymptotic stability of the origin or a globally asymptotically stable T-periodic solution.
Conclusions:
- The study provides a theoretical framework for optimizing Wolbachia-based mosquito control strategies.
- Mathematical insights into CI intensity and release dynamics are crucial for effective population suppression.
- The derived thresholds can guide practical implementation of Wolbachia interventions.
