This Demonstration describes the evolution of a microbial population. A viable cell at time

can be in one of three states at time

: divided with a probability of

, dead with a probability of

, or alive but undivided with a probability of

, where

and

are the division and mortality probability rate functions, respectively. These two functions are assumed to be logistic, that is, governed by three parameters each:

or

,

or

, and

or

, all of which have their values entered with sliders. They represent these probability rate functions' asymptotic level, rate of ascent, and the time location of the inflection point, respectively, that is,

and

. The Demonstration then calculates and plots the number of cells alive at time

,

, descendent of the specified initial number,

. The calculation is based on a version of the model for the limiting case where

tends to zero, making it continuous and fully deterministic.

You can modify the probability rate functions to create curves depicting growth, mortality, and transitions between them. You can also enter the initial number of cells,

, to calculate the number of cells at a chosen time

,

, and you can set the maximum value of the time axis in the plots. The top plot in the panel shows the chosen

and

functions and the bottom plot shows the corresponding growth and/or mortality curve,

.

J. Horowitz, M. D. Normand, M. G. Corradini, and M. Peleg, "Probabilistic Model of Microbial Cell Growth, Division and Mortality,"

*Applied and Environmental Microbiology*,

**76**(1), 2010 pp. 230–242.

M. G. Corradini, M. D. Normand, and M. Peleg, "A Stochastic and Deterministic Model of Microbial Heat Inactivation,"

*Journal of Food Science*,

**75**, 2010 pp. R59–R70.