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Mathematical Models of Cross Protection in the Epidemiology of Plant-Virus Diseases

Mathematical models of plant-virus disease epidemics were developed where cross protection occurs between viruses or virus strains. Such cross protection can occur both naturally and through artificial intervention. Examples of diseases with continuous and discontinuous crop-host availability were considered: citrus tristeza and barley yellow dwarf, respectively. Analyses showed that, in a single host population without artificial intervention, the two categories of host plants, infected with a protecting virus alone and infected with a challenging virus, could not coexist in the long term. For disease systems with continuous host availability, the virus (strain) with the higher basic reproductive number (R₀) always excluded the other eventually; whereas, for discontinuous systems, R₀ is undefined and the virus (strain) with the larger natural transmission rate was the one that persisted in the model formulation. With a proportion of hosts artificially inoculated with a protecting mild virus, the disease caused by a virulent virus could be depressed or eliminated, depending on the proportion. Artificial inoculation may be constant or adjusted in response to changes in disease incidence. The importance of maintaining a constant level of managed cross protection even when the disease incidence dropped was illustrated. Investigations of both pathosystem types showed the same qualitative result: that managed cross protection need not be 100% to eliminate the virulent virus (strain). In the process of replacement of one virus (strain) by another over time, the strongest competition occurred when the incidence of both viruses or virus strains was similar. Discontinuous crop-host availability provided a greater opportunity for viruses or virus strains to replace each other than did the more stable continuous cropping system. The process by which one Barley yellow dwarf virus replaced another in New York State was illustrated.