Bulletin of Mathematical Biology

, Volume 68, Issue 1, pp 3–23

# Traveling Waves and Spread Rates for a West Nile Virus Model

• Mark Lewis
• Joanna Rencławowicz
• P. van den Driessche
Original Article

## Abstract

A reaction–diffusion model for the spatial spread of West Nile virus is developed and analysed. Infection dynamics are based on a modified version of a model for cross infection between birds and mosquitoes (Wonham et al., 2004, An epidemiological model for West-Nile virus: Invasion analysis and control application. Proc. R. Soc. Lond. B 271), and diffusion terms describe movement of birds and mosquitoes. Working with a simplified version of the model, the cooperative nature of cross-infection dynamics is utilized to prove the existence of traveling waves and to calculate the spatial spread rate of infection. Comparison theorem results are used to show that the spread rate of the simplified model may provide an upper bound for the spread rate of a more realistic and complex version of the model.

### Keywords

West Nile virus model Traveling waves Spread rate Comparison theorems

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### References

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## Authors and Affiliations

• Mark Lewis
• 1
• 2
• Joanna Rencławowicz
• 1
• 3
• 4
• P. van den Driessche
• 4
1. 1.Department of Biological SciencesUniversity of AlbertaEdmontonCanada
2. 2.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
3. 3.Institute of MathematicsPolish Academy of SciencesWarsawPoland
4. 4.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada