A compressed logistic equation on bacteria growth: inferring time-dependent growth rate

Abstract

We propose a compressed logistic model for bacterial growth by invoking a time-dependent rate instead of the intrinsic growth rate (constant), which was adopted in traditional logistic models. The new model may have a better physiological basis than the traditional ones, and it replicates experimental observations, such as the case example for E. coli, Salmonella, and Staphylococcus aureus. Stochastic colonial growth at a different rate may have a fractal-like nature, which should be an origin of the time-dependent reaction rate. The present model, from a stochastic viewpoint, is approximated as a Gaussian time evolution of bacteria (error function).