bacteria scale
We use logistic equation to fit the mono-restrict factor growth of bacteria, and the bacteria scale itself is the factor.
dX/dt=Vmax*(1-X/Xmax)*X
Although the production is the most important, we base all of our modeling on the bacteria scale equation, since we think the production we get is a result of the whole flora. We assume that all the bacteria are the same, so that our modeling can be much easier. Actually there are several equations to fit the bacteria growth. Since our target is to increase the production in an industrial process, our fermentation takes 48h, a rather long time, with relatively abundant sources, and happens in the big fermentation cylinder. This environment means with the growth of bacteria, the scale itself is the only restrictive factor. Thus we use logistic model, the best choice to illustrate the growth with mono-restrictive factor.
In this equation, ‘X’ means the bacteria scale, it’s the function of‘t’, time. 'Vmax' represents the possible max relative growth speed of the bacteria . 'Xmax' is the upper limit of the growth. In this function, we can find out that the instantaneous growth speed is determined by the relative growth speed, upper limit of the growth, and the instantaneous scale. With time passing by, the scale grows larger, while the speed turns down.
