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Maintaining Aedes aegypti Mosquitoes Infected with Wolbachia
Published on: August 14, 2017
Discrete dynamical models on Wolbachia infection frequency in mosquito populations with biased release ratios
Yantao Shi1,2, Bo Zheng1,2
1College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, People's Republic of China.
Abstract:
We develop two discrete models to study how supplemental releases affect the Wolbachia spreading dynamics in cage mosquito populations. The first model focuses on the case when only infected males are released at each generation. This release strategy has been proved to be capable of speeding up the Wolbachia persistence by suppressing the compatible matings between uninfected individuals. The second model targets the case when only infected females are released at each generation. For both models, detailed model formulation, enumeration of the positive equilibria and their stability analysis are provided. Theoretical results show that the two models can generate bistable dynamics when there are three positive equilibrium points, semi-stable dynamics for the case of two positive equilibrium points. And when the positive equilibrium point is unique, it is globally asymptotically stable. Some numerical simulations are offered to get helpful implications on the design of the release strategy.
Insights
Supplemental releases of mosquitoes infected with Wolbachia can influence spreading dynamics. Releasing infected males or females impacts Wolbachia persistence and population stability, offering insights for control strategies.
Area of Science:
- Mathematical modeling
- Population dynamics
- Infectious disease ecology
Background:
- Wolbachia is a bacterium that can reduce mosquito lifespan and alter reproductive success.
- Controlling mosquito populations is crucial for managing vector-borne diseases.
- Supplemental releases are a strategy to introduce or enhance Wolbachia presence.
Purpose of the Study:
- To investigate the impact of supplemental releases of Wolbachia-infected mosquitoes on population dynamics.
- To compare the effects of releasing infected males versus infected females.
- To analyze the stability of Wolbachia spreading dynamics under different release scenarios.
Main Methods:
- Development of two discrete mathematical models for mosquito populations.
- Analysis of model equilibria and their stability.
- Numerical simulations to explore theoretical findings.
Main Results:
- Models predict bistable or semi-stable dynamics based on the number of positive equilibrium points.
- Unique positive equilibrium points demonstrate global asymptotic stability.
- Release strategies influence Wolbachia persistence and population dynamics.
Conclusions:
- Supplemental releases of Wolbachia-infected mosquitoes can significantly alter population dynamics.
- The choice of releasing infected males or females has distinct effects on Wolbachia spread.
- Mathematical models provide valuable insights for optimizing Wolbachia-based mosquito control strategies.
