Bulletin of Mathematical Biology

, Volume 75, Issue 9, pp 1501–1523 | Cite as

Modelling a Wolbachia Invasion Using a Slow–Fast Dispersal Reaction–Diffusion Approach

  • Matthew H. T. Chan
  • Peter S. Kim
Original Article


This paper uses a reaction–diffusion approach to examine the dynamics in the spread of a Wolbachia infection within a population of mosquitoes in a homogeneous environment. The formulated model builds upon an earlier model by Skalski and Gilliam (Am. Nat. 161(3):441–458, 2003), which incorporates a slow and fast dispersal mode. This generates a faster wavespeed than previous reaction–diffusion approaches, which have been found to produce wavespeeds that are unrealistically slow when compared with direct observations. In addition, the model incorporates cytoplasmic incompatibility between male and female mosquitoes, which creates a strong Allee effect in the dynamics. In previous studies, linearised wavespeeds have been found to be inaccurate when a strong Allee effect is underpinning the dynamics. We provide a means to approximate the wavespeed generated by the model and show that it is in close agreement with numerical simulations. Wavespeeds are approximated for both Aedes aegypti and Drosophila simulans mosquitoes at different temperatures. These wavespeeds indicate that as the temperature decreases within the optimal temperature range for mosquito survival, the speed of a Wolbachia invasion increases for Aedes aegypti populations and decreases for Drosophila simulans populations.


Invasion dynamics Wolbachia invasion Reaction–diffusion equations Strong Allee effect 



The work of MHTC was supported by the Australian Postgraduate Award. PSK was supported by the ARC Discovery Early Career Research Award.


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Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

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