A Model for the Kinetics of Phage Attachment to Bacteria in Suspension

In this paper a model is proposed for some aspects of the kinetics of phage attachment to bacteria in suspension. The model proposed is based on a construction of a set of differential equations describing the rates of change of concentrations of the various possible particles, each consisting of a bacterium with i (0 < i < r) attached phage particles. The recursive solution of this set of equations yields a discrete distribution of the bacteria according to the number of phage particles attached to each of them. This distribution, although it is timedependent and has a finite set of values, is similar to Greenwood-YulePolya's [1920, 1930] Negative Binomial. Contagious distributions have been classified by Gurland [1958], Beall and Rescia [1953] and others, mainly, through the use of compounding procedures. The fact that our assumptions lead to a hypothesis of true contagion, as defined by Feller [1943], has suggested the desirability of direct derivation of the descriptive equations. Certain assumptions regarding the parameters permit the formulation of simplified equations among which the non-degenerate ones are similar to the Binomial, the Geometric and the Poisson distributions. Experimental data will be given in a future paper in which fitting the distribution will be discussed.