Modelling Microbial Growth. Probabilistic Aspects.
by
Tanya Soboleva
AgResearch, Ruakura
Coauthors: Tony Pleasants

Current models of microbe growth assumes it is a deterministic process. This neglects fluctuations of environmental factors and intrinsic noise connected with discreteness of growth process as well. Our approach describes microbial growth as a stongly non-linear stochastic process. Starting from a stochastic differential equation which is constructed to describe properly experimental situation we derive an equation for the evolution of the probability density function for the process. An analytical solution of this Fokker-Planck equation corresponding to Gaussian initial conditions has been found. It describes the evolution of a population, which has an initial Gaussian density towards the asymmetrical steady-state distribution.

The probability that the random process of microbial growth will exceed some critical level was evaluated . An expression for the corresponding first passage time has been obtained in an analitical form also.

Date received: February 11, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacc-07.