A sharp dichotomy for Wolbachia invasion: Critical release thresholds and global stability

Area of Science:

• Ecology and Evolutionary Biology
• Mathematical Biology
• Vector-borne Disease Control

Background:

• Wolbachia-infected mosquitoes are used for biocontrol against mosquito-borne diseases.
• Periodic release of infected males aims to accelerate population replacement.
• This strategy leads to complex non-autonomous difference equation models.

Purpose of the Study:

• Investigate Wolbachia invasion dynamics under periodic male-only release strategies.
• Develop a mathematical framework to analyze the complex population dynamics.
• Identify conditions for successful and stable Wolbachia population replacement.

Main Methods:

• Utilized Poincaré map theory and geometric analysis.
• Developed a novel framework to handle analytically challenging difference equations.
• Identified a critical release threshold (α*) governing system behavior.

Main Results:

• A critical release threshold (α*) was identified, determining system dynamics.
• Above α*, Wolbachia-fixed equilibrium achieves global stability, ensuring population replacement.
• Below α*, the system exhibits bistability, indicating potential for incomplete replacement.

Conclusions:

• Established a quantitative criterion for optimizing Wolbachia release strategies.
• Overcame computational obstacles in non-autonomous systems.
• Provided practical guidance for designing effective Wolbachia-based disease control programs.