Bulletin of Mathematical Biology

, Volume 68, Issue 1, pp 3–23

Traveling Waves and Spread Rates for a West Nile Virus Model

Authors

  • Mark Lewis
    • Department of Biological SciencesUniversity of Alberta
    • Department of Mathematical and Statistical SciencesUniversity of Alberta
    • Department of Biological SciencesUniversity of Alberta
    • Institute of MathematicsPolish Academy of Sciences
    • Department of Mathematics and StatisticsUniversity of Victoria
  • P. van den Driessche
    • Department of Mathematics and StatisticsUniversity of Victoria
Original Article

DOI: 10.1007/s11538-005-9018-z

Cite this article as:
Lewis, M., Rencławowicz, J. & den Driessche, P.v. Bltn. Mathcal. Biology (2006) 68: 3. doi:10.1007/s11538-005-9018-z

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 modelTraveling wavesSpread rateComparison theorems

Copyright information

© Springer Science+Business Media, Inc. 2005