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Dynamical systems analysis of a model describing Tasmanian devil facial tumour disease
journal contribution
posted on 2023-05-17, 18:23 authored by Nicholas Beeton, Lawrence ForbesLawrence ForbesA 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.
History
Publication title
The ANZIAM JournalVolume
54Issue
1-2Pagination
89-107ISSN
1446-1811Department/School
School of Natural SciencesPublisher
Australian Mathematics Publ Assoc IncPlace of publication
Mathematics Dept Australian National Univ, Canberra, Australia, Act, 0200Rights statement
Copyright 2012 Australian Mathematics Publ Assoc IncRepository Status
- Restricted