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Wolbachia Invasion in Mosquitoes with Incomplete CI, Imperfect Maternal Transmission and Maturation Delay

Xiaoke Ma1, Ying Su2

  • 1Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, People's Republic of China.

Bulletin of Mathematical Biology
|October 14, 2024
PubMed

Insights

This study explores Wolbachia invasion dynamics in mosquitoes using a mathematical model. It identifies conditions for successful invasion and suppression, revealing complex system behaviors like bistability influenced by maturation delay.

Area of Science:

  • Mathematical Biology
  • Vector-borne Disease Ecology
  • Microbial Genetics

Background:

  • Cytoplasmic incompatibility (CI) is a key factor in Wolbachia's spread in wild mosquito populations.
  • Previous models, like Su et al.'s delay differential equation, link CI to maturation delays.
  • Understanding these dynamics is crucial for controlling mosquito-borne diseases.

Purpose of the Study:

  • To investigate the dynamics of a Wolbachia invasion model with density-dependent and independent death rates.
  • To determine conditions for Wolbachia invasion success and suppression under varying maternal transmission rates.
  • To analyze the impact of maturation delay on system stability and bistability.

Main Methods:

  • Analysis of equilibrium existence and stability in a delay differential equation model.
  • Investigation of model dynamics under perfect and imperfect maternal transmission scenarios.
  • Numerical simulations to explore monostable and bistable behaviors and the role of maturation delay.

Main Results:

  • Parameter conditions for successful Wolbachia invasion with perfect maternal transmission were derived.
  • Ranges for invasion failure, success, and partial suppression were identified for imperfect transmission.
  • The study revealed monostable and bistable dynamics, with maturation delay influencing a unique unstable separatrix in bistable scenarios.

Conclusions:

  • The mathematical model provides insights into Wolbachia invasion dynamics and potential control strategies.
  • Maturation delay plays a significant role in the system's stability and the emergence of bistability.
  • Further research into these complex dynamics can inform vector control efforts.
Keywords:
Wolbachia infectionBistable phenomenonCytoplasmic incompatibilityDelay differential equationMaternal transmissionPopulation replacement

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