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Global dynamics of a reaction and diffusion model for Lyme disease

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Abstract

This paper is devoted to the mathematical analysis of a reaction and diffusion model for Lyme disease. In the case of a bounded spatial habitat, we obtain the global stability of either disease-free or endemic steady state in terms of the basic reproduction number R 0. In the case of an unbounded spatial habitat, we establish the existence of the spreading speed of the disease and its coincidence with the minimal wave speed for traveling fronts. Our analytic results show that R 0 is a threshold value for the global dynamics and that the spreading speed is linearly determinate.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada

    Xiao-Qiang Zhao

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  1. Xiao-Qiang Zhao
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Correspondence to Xiao-Qiang Zhao.

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Research supported in part by the NSERC of Canada and the MITACS of Canada.

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Zhao, XQ. Global dynamics of a reaction and diffusion model for Lyme disease. J. Math. Biol. 65, 787–808 (2012). https://doi.org/10.1007/s00285-011-0482-9

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  • DOI: https://doi.org/10.1007/s00285-011-0482-9

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