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Modelling a Wolbachia invasion using a slow-fast dispersal reaction-diffusion approach
Matthew H T Chan1, Peter S Kim
1School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia. M.Chan@maths.usyd.edu.au
Bulletin of Mathematical Biology
|June 13, 2013
Summary
This study models Wolbachia infection spread in mosquitoes using reaction-diffusion. A new model with dual dispersal and Allee effect accurately predicts faster invasion wavespeeds, varying with temperature for different mosquito species.
Area of Science:
- Mathematical modeling of infectious disease dynamics.
- Population genetics and evolutionary biology.
- Vector-borne disease control strategies.
Background:
- Understanding the spatial spread of Wolbachia infections is crucial for mosquito population control.
- Previous reaction-diffusion models produced unrealistically slow invasion wavespeeds.
- The Allee effect, driven by cytoplasmic incompatibility, significantly impacts invasion dynamics.
Purpose of the Study:
- To develop and analyze a reaction-diffusion model for Wolbachia spread incorporating slow/fast dispersal and a strong Allee effect.
- To accurately approximate and validate the model's predicted invasion wavespeeds.
- To investigate the influence of temperature on Wolbachia invasion speed in Aedes aegypti and Drosophila simulans.
Main Methods:
- Formulation of a novel reaction-diffusion model building on Skalski and Gilliam (2003).
- Incorporation of a dual dispersal mode (slow and fast) to enhance wavespeed realism.
- Inclusion of cytoplasmic incompatibility to model a strong Allee effect.
- Development of an analytical approximation for wavespeed, validated against numerical simulations.
Main Results:
- The model generates faster wavespeeds compared to previous reaction-diffusion approaches.
- The approximated wavespeed closely matches numerical simulation results.
- Temperature influences Wolbachia invasion speed differently: increasing for Aedes aegypti and decreasing for Drosophila simulans within their optimal temperature ranges.
Conclusions:
- The developed model provides a more accurate framework for predicting Wolbachia invasion dynamics.
- The interplay between dispersal, Allee effect, and temperature is critical for understanding invasion speed.
- Findings have implications for optimizing Wolbachia-based mosquito control strategies across different environments and species.
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