Team:Nankai/Modeling

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Power House

3 models are used to measure our project.

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

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.

Product scale

We assume that our product comes from two parts, one is during the growth, and the other is through their livelihood.

dP/dt=α*dX/dt+β*X
Substrate scale

Bacteria use the provided carbon source to propagate, maintain their livelihood and synthesize the product.

dS/dt=-γ*dX/dt-δ*X-ε*dP/dt
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