Dynamical systems analysis of a model describing Tasmanian Devil Facial Tumour Disease

Nicholas Jeffrey Beeton, Larry Forbes

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.

doi:10.1017/S1446181113000011

Keywords


Tasmanian devil, epidemic model, nonlinear dynamics, stability, Hopf bifurcation



DOI: http://dx.doi.org/10.21914/anziamj.v54i0.5439



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.