Article

# Modelling Vector Transmission and Epidemiology of Co-Infecting Plant Viruses

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Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA
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Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA
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Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK
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IGEPP, Agrocampus Ouest, INRA, Université de Rennes 1, Université Bretagne-Loire, 35000 Rennes, France
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Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrück University, 49069 Osnabrück, Germany
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Centre for Environmental Policy, Imperial College London, Ascot SL5 7PY, UK
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Author to whom correspondence should be addressed.
Received: 5 November 2019 / Revised: 3 December 2019 / Accepted: 6 December 2019 / Published: 13 December 2019
(This article belongs to the Special Issue Plant Virus Transmission by Vectors)
Co-infection of plant hosts by two or more viruses is common in agricultural crops and natural plant communities. A variety of models have been used to investigate the dynamics of co-infection which track only the disease status of infected and co-infected plants, and which do not explicitly track the density of inoculative vectors. Much less attention has been paid to the role of vector transmission in co-infection, that is, acquisition and inoculation and their synergistic and antagonistic interactions. In this investigation, a general epidemiological model is formulated for one vector species and one plant species with potential co-infection in the host plant by two viruses. The basic reproduction number provides conditions for successful invasion of a single virus. We derive a new invasion threshold which provides conditions for successful invasion of a second virus. These two thresholds highlight some key epidemiological parameters important in vector transmission. To illustrate the flexibility of our model, we examine numerically two special cases of viral invasion. In the first case, one virus species depends on an autonomous virus for its successful transmission and in the second case, both viruses are unable to invade alone but can co-infect the host plant when prevalence is high. View Full-Text
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MDPI and ACS Style

Allen, L.J.S.; Bokil, V.A.; Cunniffe, N.J.; Hamelin, F.M.; Hilker, F.M.; Jeger, M.J. Modelling Vector Transmission and Epidemiology of Co-Infecting Plant Viruses. Viruses 2019, 11, 1153. https://0-doi-org.brum.beds.ac.uk/10.3390/v11121153

AMA Style

Allen LJS, Bokil VA, Cunniffe NJ, Hamelin FM, Hilker FM, Jeger MJ. Modelling Vector Transmission and Epidemiology of Co-Infecting Plant Viruses. Viruses. 2019; 11(12):1153. https://0-doi-org.brum.beds.ac.uk/10.3390/v11121153

Chicago/Turabian Style

Allen, Linda J.S., Vrushali A. Bokil, Nik J. Cunniffe, Frédéric M. Hamelin, Frank M. Hilker, and Michael J. Jeger 2019. "Modelling Vector Transmission and Epidemiology of Co-Infecting Plant Viruses" Viruses 11, no. 12: 1153. https://0-doi-org.brum.beds.ac.uk/10.3390/v11121153

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