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

Huichao Yang1, Deyu Kong1, Jianshe Yu2

  • 1School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China.

Mathematical Biosciences
|April 27, 2026
PubMed

Insights

Introducing Wolbachia-infected mosquitoes is a biocontrol strategy for mosquito-borne diseases. A critical release threshold determines successful population replacement, with ratios above it ensuring Wolbachia 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.
Keywords:
Critical release thresholdGlobal stabilityPopulation replacementWolbachia invasion

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