Some Stochastic Models Relating Time and Dosage in Response Curves

Abstract

SUMMARY Two models are proposed to aid in the interpretation of the functional relationship between time and dilution in micro-organism-host systems. The Collective Action Model leads to, (i) Multi-hit time dependent dosage response curves, except for limiting times where it is one-hit, and (ii) An approximately linear relationship between the mean incubation time and the logarithm of the dilution whenever the dose is large. The Individual Action Model leads to, (i) One-hit time dependent dosage response curves for all incubation times, and (ii) An approximately linear relationship between the logarithm of the median of the inicubation times and the logarithm of the dilution whenever the dose is very large. It is suggested that these models may be graphically distinguished by using these results. The graphs, if they show a good fit to either model, will yield crude estimates of the parameters of the micro-organism growth process, that is, the multiplication rate and the critical population size. It must be noted, of course, that these two models ignore various complications (such as host variability, for instance) and canniot be proposed as the only possible models for such experimental systems.