Association of logistic and Poisson models of infection with some physical characteristics of a single component plant virus

A logistic model was recently formulated to describe the relationship between concentration of a single component plant virus and infections produced by inoculation to a local lesion host. In this paper the logistic is combined with a Poisson model. The logistic makes accurate fitting possible for a variety of infection-dilution series; and the Poisson acts as a base line, indicating whether lesion numbers are compatible with the hypothesis that random infection of similar infection sites has occurred. A logarithmic form of the logistic equation gives a straight line with negative slope (logit slope) which is useful in characterizing dilution series to which the logistic is fitted. A modified Poisson equation can also be fitted to a range of dilution series; it provides an independent estimate of slope for curves not widely divergent from the standard Poisson. Models have also been developed to define the limits of concentration within which single virions are likely to be randomly dispersed in inoculum without immediate contact with other virions, and are therefore more likely to enter inoculated tissue independently and cause random infections. Models are formulated for aggregation of tobacco mosaic virus in monolayers, crystals, and lenticular aggregates. Published and unpublished data are fitted and analyzed using some of these models.