Journal Article

A model for analysing plant-virus transmission characteristics and epidemic development

M. J. JEGER, F. van den BOSCH, L. V. MADDEN and J. HOLT

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 15, issue 1, pages 1-18
Published in print March 1998 | ISSN: 1477-8599
Published online March 1998 | e-ISSN: 1477-8602 | DOI:
A model for analysing plant-virus transmission characteristics and epidemic development

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  • Applied Mathematics
  • Biomathematics and Statistics


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Most plant viruses are vectored by arthropods, often Homopteran insects. Four general classes of plant-virus diseases have been recognized; they are distinguished by the transmission characteristics and the nature of the interaction of the virus with the vector. For nonpersistently transmitted viruses, the virus is usually restricted to the stylet of the insect. For persistently transmitted viruses, the virus is ingested, passes through the gut wall into the haemolymph, and then moves to the salivary glands where it can potentially be transmitted to other plants. Persistently transmitted viruses, have two subclasses termed circulaive if there is no multiplication in the insect vector and propagative if there is. A fourth class, semipersistent, which is intermediate between nonpersistent and persistent, is generally recognized; in this class the virus moves to the foregut of the insect. A model has been developed in which an SEIR-type epidemic for the host plant is linked with the insect vector population (an SEI model with vertical transmission) to describe the transmission process. This model was used to compare the transmission characteristics of the four virus classes directly, and to explore the consequences for epidemic development and possible control options. Depending on the assumptions made about migration, it was possible to obtain an expression for the basic reproductive number, R0. Expressions were also obtained for equilibrium values for the host and vector population classes; and a numerical analysis indicated that these equilibria were stable for known or reasonable estimates of the parameter values. The basic reproductive number, R0, was used to examine the relative contributions of key parameters in distinguishing the four virus disease classes using parameter values and ranges taken directly from the literature or estimated indirectly. Pairwise plots of parameter values which satisfied the threshold criterion R0 = 1 clearly separated the propagative class from the other categories. On holding the other parameters constant, a much larger vector population or vector activity was required to satisfy the epidemic threshold for propagative viruses. Similar conclusions were reached from plots of the healthy host and viruliferous vector populations against key parameters. The model framework was used to analyse the effectiveness of roguing (the removal and destruction) of diseased plants and/or reduction of the vector-population size, for example, by insecticide treatment or vegetation management. Roguing would only be effective for nonpersistently transmitted viruses at relatively low vector-population densities. Roguing would usually only be needed for propagative viruses at very high population densities. There would be a clear advantage in reducing the vector-population density for propagative viruses, and control measures aimed at reducing populations would only be effective for these viruses.

Keywords: plant-virus epidemiology; nonpersistent transmission; persistent transmission; vector population density; vector activity; basic reproductive number; disease control

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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