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Dynamical systems analysis of a model describing Tasmanian devil facial tumour disease

Citation

Beeton, NJ and Forbes, LK, Dynamical systems analysis of a model describing Tasmanian devil facial tumour disease, The ANZIAM Journal, 54, (1-2) pp. 89-107. ISSN 1446-1811 (2012) [Refereed Article]


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Copyright Statement

Copyright 2012 Australian Mathematics Publ Assoc Inc

DOI: doi:10.1017/S1446181113000011

Abstract

A susceptible–exposed–infectious theoretical model describing Tasmanian devil population and disease dynamics is presented and mathematically analysed using a dynamical systems approach to determine its behaviour under a range of scenarios. The steady states of the system are calculated and their stability analysed. Closed forms for the bifurcation points between these steady states are found using the rate of removal of infected individuals as a bifurcation parameter. A small-amplitude Hopf region, in which the populations oscillate in time, is shown to be present and subjected to numerical analysis. The model is then studied in detail in relation to an unfolding parameter which describes the disease latent period. The model’s behaviour is found to be biologically reasonable for Tasmanian devils and potentially applicable to other species.

Item Details

Item Type:Refereed Article
Keywords:Tasmanian devil, epidemic model, nonlinear dynamics, stability, Hopf bifurcation
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Biological Mathematics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Beeton, NJ (Dr Nicholas Beeton)
Author:Forbes, LK (Professor Larry Forbes)
ID Code:85107
Year Published:2012
Web of Science® Times Cited:1
Deposited By:Research Division
Deposited On:2013-06-14
Last Modified:2015-03-04
Downloads:4 View Download Statistics

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