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A model for the treatment of environmentally transmitted sarcoptic mange in bare-nosed wombats (Vombatus ursinus)

Beeton, NJ ORCID: 0000-0002-8513-3165, Carver, S ORCID: 0000-0002-3579-7588 and Forbes, LK ORCID: 0000-0002-9135-3594 2019 , 'A model for the treatment of environmentally transmitted sarcoptic mange in bare-nosed wombats (Vombatus ursinus)' , Journal of Theoretical Biology, vol. 462 , pp. 466-474 , doi: 10.1016/j.jtbi.2018.11.033.

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Abstract

Some of the most important wildlife diseases involve environmental transmission, with disease control attempted via treatments that induce temporary pathogen resistance among hosts. However, theoretical explanations of such circumstances remain few.A mathematical model is proposed and investigated to analyse the dynamics and treatment of environmentally transmitted sarcoptic mange in a population of bare-nosed wombats. The wombat population is structured into four classes representing stages of infection, in a model that consists of five non-linear differential equations including the unattached mite population. It is shown that four different epidemiological outcomes are possible. These are: (1) extinction of wombats (and mites); (2) mite-free wombat populations; (3) endemic wombats and mites coexisting, with the wombats’ population reduced below the environmental carrying capacity; and (4) a stable limit cycle (sustained oscillating populations) with wombat population far below carrying capacity. Empirical evidence exists for the first two of these outcomes, with the third highly likely to occur in nature, and the fourth plausible at least until wombat populations succumb to Allee effects. These potential outcomes are examined to inform treatment programs for wombat populations. Through this theoretical exploration of a relatively well understood empirical system, this study supports general learning across environmentally transmitted wildlife pathogens, increasing understanding of how pathogen dynamics may cause crashes in some populations and not others.

Item Type: Article
Authors/Creators:Beeton, NJ and Carver, S and Forbes, LK
Keywords: wildlife disease, dynamical systems analysis, susceptible-exposed-infected-recovered; wombats
Journal or Publication Title: Journal of Theoretical Biology
Publisher: Academic Press Ltd Elsevier Science Ltd
ISSN: 0022-5193
DOI / ID Number: 10.1016/j.jtbi.2018.11.033
Copyright Information:

Copyright 2018 Elsevier Ltd.

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