Strathprints Home | Open Access | Browse | Search | User area | Copyright | Help | Library Home | SUPrimo

The characteristics of epidemics and invasions with thresholds

Cruickshank, I. and Gurney, William and Veitch, A.R. (1999) The characteristics of epidemics and invasions with thresholds. Theoretical Population Biology, 56 (3). pp. 279-292. ISSN 0040-5809

[img]
Preview
PDF - Published Version
Download (369Kb) | Preview

    Abstract

    In this paper we report the development of a highly efficient numerical method for determining the principal characteristics (velocity, leading edge width, and peak height) of spatial invasions or epidemics described by deterministic one-dimensiohal reaction–diffusion models whose dynamics include a threshold or Allee effect. We prove that this methodology produces the correct results for single-component models which are generalizations of the Fisher model, and then demonstrate by numerical experimentation that analogous methods work for a wide class of epidemic and invasion models including the S–I and S–E–I epidemic models and the Rosenzweig–McArthur predator–prey model. As examplary application of this approach we consider the atto–fox effect in the classic reaction–diffusion model of rabies in the European fox population and show that the appropriate threshold for this model is within an order of magnitude of the peak disease incidence and thus has potentially significant effects on epidemic properties. We then make a careful re-parameterisation of the model and show that the velocities calculated with realistic thresholds differ surprisingly little from those calculated from threshold-free models. We conclude that an appropriately thresholded reaction–diffusion model provides a robust representation of the initial epidemic wave and thus provides a sound basis on which to begin a properly mechanistic modelling enterprise aimed at understanding the long-term persistence of the disease.

    Item type: Article
    ID code: 41807
    Keywords: epidemics , invasions, thresholds, Probabilities. Mathematical statistics, Biology, Ecology, Evolution, Behavior and Systematics
    Subjects: Science > Mathematics > Probabilities. Mathematical statistics
    Science > Natural history > Biology
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
      Depositing user: Pure Administrator
      Date Deposited: 29 Oct 2012 16:00
      Last modified: 05 Sep 2014 18:37
      URI: http://strathprints.strath.ac.uk/id/eprint/41807

      Actions (login required)

      View Item

      Fulltext Downloads: