Mathematical models of cross protection in the epidemiology of plant-virusdiseases

Mathematical models of plant-virus disease epidemics were developed where c ross protection occurs between viruses or virus strains. Such cross protect ion can occur both naturally and through artificial intervention. Examples of diseases with continuous and discontinuous crop-host availability were c onsidered: citrus tristeza and barley yellow dwarf, respectively. Analyses showed that, in a single host population without artificial intervention, t he two categories of host plants, infected with a protecting virus alone an d infected with a challenging virus, could not coexist in the long term. Fo r disease systems with continuous host availability, the virus (strain) wit h the higher basic reproductive number (R-0) always excluded the other even tually; whereas, for discontinuous systems, R-0 is undefined and the virus (strain) with the larger natural transmission rate was the one that persist ed in the model formulation. With a proportion of hosts artificially inocul ated with a protecting mild virus, the disease caused by a virulent virus c ould be depressed or eliminated, depending on the proportion. Artificial in oculation may be constant or adjusted in response to changes in disease inc idence. The importance of maintaining a constant level of managed cross pro tection even when the disease incidence dropped was illustrated. Investigat ions of both pathosystem types showed the same qualitative result: that man aged cross protection need not be 100% to eliminate the virulent virus (str ain). In the process of replacement of one virus (strain) by another over t ime, 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 t han did the more stable continuous cropping system. The process by which on e Barley yellow dwarf virus replaced another in New York State was illustra ted.