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Nonlinear diffusion and viral spread through the leaf of a plant

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Abstract

The spread of a virus through the leaf of a plant is both spatially and temporally causal in that the present status depends on the past and the spatial spread is compactly supported and progresses outwards. Such spatial spread is known to occur for certain nonlinear diffusion processes. The first compactly supported solution for nonlinear diffusion equations appears to be that of Pattle published in 1959. In that paper, no explanation is given as to how the solution was derived. Here, we show how the solution can be derived using Lie symmetry analysis. This lays a foundation for exploring the behavior of other choices for nonlinear diffusion and exploring the addition of reaction terms which do not eliminate the compactly supported structure. The implications associated with using the reaction–diffusion equation to model the spatial–temporal spread of a virus through the leaf of a plant are discussed.

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Authors and Affiliations

  1. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia

    Maureen P. Edwards

  2. Centre for Tropical Crops and Biocommodities, Queensland University of Technology, Brisbane, QLD, 4001, Australia

    Peter M. Waterhouse

  3. School of Mathematics, Trinity College Dublin, Dublin 2, Ireland

    María Jesús Munoz-Lopez

  4. CSIRO Data61, GPO Box 664, Canberra, ACT, 2601, Australia

    Robert S. Anderssen

  5. Department of Mathematics and Statistics, La Trobe University, Melbourne, VIC, 3086, Australia

    Robert S. Anderssen

Authors
  1. Maureen P. Edwards
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  2. Peter M. Waterhouse
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  3. María Jesús Munoz-Lopez
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  4. Robert S. Anderssen
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Corresponding author

Correspondence to Maureen P. Edwards.

Additional information

Dedicated to Jim Hill on his 70th birthday

This article is part of the topical collection “James Hill” guest edited by Scott McCue and Natalie Thamwattana.

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Edwards, M.P., Waterhouse, P.M., Munoz-Lopez, M.J. et al. Nonlinear diffusion and viral spread through the leaf of a plant. Z. Angew. Math. Phys. 67, 112 (2016). https://doi.org/10.1007/s00033-016-0707-2

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  • DOI: https://doi.org/10.1007/s00033-016-0707-2

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