modelling bacterial growth

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A number of different mathematical models have been put forward with regard to this growth curve.

The oldest, and most widely known of these, the Monod model, is still the most commonly used. The Monod model is an empirical model that accurately covers phases 2 and 3, very similar to the Michaelis Merten law on enzymatic reactions. It is written as follows

Formula: modelling bacterial growth - Monod model

KS refers to a threshold concentration below which the growth rate becomes very dependent on substrate concentration.This constant has the value S where

Formula: modelling bacterial growth - KS

is usally small but frequently greater than the levels set by discharge standards.

It must be emphasized that, in the case of bacterial cultures that use different strains of micro-organisms, the m measured is, in fact, the overall m.At a given moment, some bacteria may have achieved a growth level that is different to that of other bacteria.

In order to cover phases 4 and 5, we need to add terms that represent bacteria lysis kinetics (mortality) see also page 2 of suspended growth (activated sludge)).