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Asymptotic analysis of an epidemic model with primary and secondary infection

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Abstract

For many biological systems, the behavior of interest is contained in the evolution of transients rather than in the stability of equilibria. These include systems in which perturbations and interruptions occur on a time scale much shorter than the equilibration time, and those in which any final equilibrium is sensitive to initial conditions. In this article, we examine a model of fungal root disease in a crop involving primary and secondary infection mechanisms. This system is subject to regular interruptions in the form of harvesting and sowing. Using an asymptotic approach in which certain parameter values are assumed to be small, the model can be broken down into a set of simpler subsystems respresenting recognizable biological mechanisms. These linear models can be solved to give closed-form analytical solutions for transient evolution. From this information, it is possible to construct an annual map of disease severity in the crop, and determine the parameter values under which the infection will bulk up or fade out.

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Authors and Affiliations

  1. Department of Plant Sciences, University of Cambridge, Downing Street, CB2 3EA, Cambridge, U.K.

    J. E. Truscott, C. R. Webb & C. A. Gilligan

  2. IACR Broom's Barn, Higham, Bury St. Edmunds, IP28 6NP, Suffolk, U.K.

    J. E. Truscott & C. R. Webb

Authors
  1. J. E. Truscott
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  2. C. R. Webb
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  3. C. A. Gilligan
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Correspondence to J. E. Truscott.

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Truscott, J.E., Webb, C.R. & Gilligan, C.A. Asymptotic analysis of an epidemic model with primary and secondary infection. Bltn Mathcal Biology 59, 1101–1123 (1997). https://doi.org/10.1007/BF02460103

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  • DOI: https://doi.org/10.1007/BF02460103

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