Abstract
A model for indirect vector transmission and epidemic development of plant viruses is extended to consider direct transmission through vector mating. A basic reproduction number is derived which is the sum of the R0 values specific for three transmission routes. We analyse the model to determine the effect of direct transmission on plant disease control directed against indirect transmission. Increasing the rate of horizontal sexual transmission means that vector control rate or indirect transmission rate must be increased/decreased substantially to maintain R0 at a value less than 1. By contrast, proportionately increasing the probability of transovarial transmission has little effect. Expressions are derived for the steady-state values of the viruliferous vector population. There is clear advantage for an insect virus in indirect transmission to plants, especially where the sexual and transovarial transmission rates are low; however information on virulence–transmissibility relationships is required to explain the evolution of a plant virus from an insect virus.
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