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 Published and unpublished data are fitted and analyzed using some of these models.

Logistic and Poisson models for infection by multicomponent plant viruses.

A model for the relationship between virus concentration and infectivity of multicomponent plant viruses is based on a combination of logistic and Poisson equations. Two separate equations are derived from the Poisson distribution assuming, (i) that infections occur only when a set of components containing the complete multicomponent genome is established at an infection site, but that any excess of components present does not reduce the probability of infection (no interference postulate); and (ii) that infection can occur only if a set of components containing the full genome reaches an infection site before it can be preempted by an incomplete set (competitive interference postulate). Postulate (i) affects the form of a dilution series without affecting N, the maximum possible number of infections (lesions), and postulate (ii) changes the value of N but not the form of the dilution series. There is a close correlation between the logit slope of a logistic dilution series and the form of the corresponding multiple Poisson dilution series for viruses with 2, 3 or 4 components. Calibrated by Poisson equations, the logit slope may thus suggest whether or not the virus components have invaded independently and infected similar infection sites. The methods of fitting the combined logistic-Poisson model are demonstrated by applying it to data for cowpea chlorotic mottle virus.

Relationship between plant virus concentration and infectivity: a 'growth curve' model.

A logistic ('growth curve') model is formulated and applied to the relationship between numbers of infections (local lesions) produced by a virus on inoculated plants and the concentration of the virus in the inoculum. This model has the advantages of being simple, data-based and therefore not founded on limiting postulates, and of being applicable to a wide range of infection-dilution series, including those obtained from multicomponent viruses. Here, it is applied to common tobacco mosaic virus. Examples of infection-dilution series taken from the literature are fitted more closely and more objectively than they were fitted by the original authors. A limiting number for lesions is estimated by minimizing chi 2 values for differences between observed lesion numbers and those calculated from the logistic equation. The complete fitting procedure can be programmed on a hand-held calculator.