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.