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Zoonotic Transmission of Waterborne Disease: A Mathematical Model

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Abstract

Waterborne parasites that infect both humans and animals are common causes of diarrhoeal illness, but the relative importance of transmission between humans and animals and vice versa remains poorly understood. Transmission of infection from animals to humans via environmental reservoirs, such as water sources, has attracted attention as a potential source of endemic and epidemic infections, but existing mathematical models of waterborne disease transmission have limitations for studying this phenomenon, as they only consider contamination of environmental reservoirs by humans. This paper develops a mathematical model that represents the transmission of waterborne parasites within and between both animal and human populations. It also improves upon existing models by including animal contamination of water sources explicitly. Linear stability analysis and simulation results, using realistic parameter values to describe Giardia transmission in rural Australia, show that endemic infection of an animal host with zoonotic protozoa can result in endemic infection in human hosts, even in the absence of person-to-person transmission. These results imply that zoonotic transmission via environmental reservoirs is important.

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Notes

  1. Possums are native Australian marsupials, here assumed to be of Trichosurus vulpecula species.

  2. This approach was used because of the lack of reliable estimates of \(\gamma _\mathrm{H}\) and \(\beta _\mathrm{H}\) in the literature. Estimates of the duration of G. lamblia infection in humans only describe the duration of symptoms (Gibney et al. 2014; Rendtorff 1954; Robertson et al. 2010), not infectiousness as defined in this paper, and vary substantially from 2 to 60 days (Gibney et al. 2014; Nash et al. 1987; Nygård et al. 2006).

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Authors and Affiliations

  1. School of Medicine, The University of Notre Dame Australia, 160 Oxford St, Darlinghurst, NSW, 2010, Australia

    Edward K. Waters

  2. The University of Melbourne, Dookie Campus, Dookie Nalinga Road, Dookie College, VIC, 3647, Australia

    Andrew J. Hamilton

  3. School of Physical, Environmental and Mathematical Sciences, The University of New South Wales Canberra, The Australian Defence Force Academy, PO Box 7916, Canberra, BC, 2610, Australia

    Harvinder S. Sidhu & Leesa A. Sidhu

  4. SMART Infrastructure Facility, University of Wollongong, Northfields Avenue, Wollongong, NSW, 2522, Australia

    Michelle Dunbar

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Correspondence to Edward K. Waters.

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Waters, E.K., Hamilton, A.J., Sidhu, H.S. et al. Zoonotic Transmission of Waterborne Disease: A Mathematical Model. Bull Math Biol 78, 169–183 (2016). https://doi.org/10.1007/s11538-015-0136-y

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