In plant-virus disease epidemiology, dynamical models have invariably incorporated a bilinear inoculation rate that is directly proportional to both the abundance of healthy (susceptible) hosts and the abundance of infective vectors. Similarly, the acquisition rate is usually assumed to be directly proportional to the abundance of nonviruliferous vectors and that of infectious hosts. These bilinear assumptions have been questioned for certain human diseases, and infection rates that incorporate power parameters of the variables have been proposed. Here, infection rates for plant-virus diseases that are of a more general form than the familiar bilinear terms are examined. For such diseases, the power parameter can be regarded as a measure of the spatial aggregation of the vectors or as a coefficient of interference between them, depending on the context.Field data of cassava mosaic virus disease (CMD) incidence were examined. When vector population density and disease incidence were high, disease progress curves over the first 6 months from planting could not be explained using models with bilinear infection rates. Incorporation of the new infection terms allowed the range of observed disease progress curve types to be described. New evidence of a mutually beneficial interaction between the viruses causing CMD and the whitefly vector, Bemisia tabaci, has shown that spatial aggregation of the vectors is an inevitable consequence of infection, particularly with a severe virus strain or a sensitive host. Virus infection increases both vector fecundity and the density of vectors on diseased plants. It is postulated that this enhances disease spread by causing an increased emigration rate of infective vectors to other crops. Paradoxically, within the infected crop, vector aggregation reduces the effective contact rate between vector and host and therefore the predicted disease incidence is less than when a bilinear contact rate is used.
Many virus diseases of plants are caused by a synergistic interaction between viruses within the host plant. Such synergism can induce symptoms more severe than would be caused by additive effects. In a synergistic interaction, the virus titre of both, one, or neither virus may be enhanced and, as a consequence, the rate of disease spread may be affected. An epidemiological model was developed in which transmission and loss rates were attributed to the different virus infection possibilities. Sharing the same host population implies competition, and this imposes an increased constraint on the survival of both viruses. It was shown that, in order to ensure virus survival in a mixed infection, the basic reproductive number should exceed a critical value which is larger than unity (R 0 . R c . 1). Here R 0 is used in the same sense as in the absence of superinfection. Increased virulence (equivalent to disease severity) in dually infected plants decreases the opportunities for both viruses to coexist, while increased virus transmission from dually infected plants increases such opportunities. The net effect of increased virulence and increased virus transmission on virus persistence was neutral if synergism caused the same proportional effect on both. Total host abundance was, however, reduced. The opportunity for virus persistence was increased if the enhancement of transmission exceeded that of virulence. Indeed, by this mechanism a virus which was nonviable alone could invade and persist in a chronic epidemic of another virus. Where the effect on virulence is greater than that on transmission, the viruses are likely to exclude each other, especially when the transmission rates of both viruses have intermediate values. In such cases, the final outcome is determined by both the parameter values and the initial state.
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