  Cross-protection, which refers to a process whereby artificially inoculating
a plant with a mild strain provides protection against a more aggressive
isolate of the virus, is known to be an effective tool of disease control in
plants. In this paper we derive and analyse a new mathematical model of the
interactions between two competing viruses with particular account for RNA
interference. Our results show that co-infection of the host can either
increase or decrease the potency of individual infections depending on the
levels of cross-protection or cross-enhancement between different viruses.
Analytical and numerical bifurcation analyses are employed to investigate the
stability of all steady states of the model in order to identify parameter
regions where the system exhibits synergistic or antagonistic behaviour between
viral strains, as well as different types of host recovery. We show that not
only viral attributes but also the propagating component of RNA-interference in
plants can play an important role in determining the dynamics.
