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Re: [Phys-l] Bacteria problem



I also thought of "collapse" (Jarred Diamond) and a more interesting maths. prob. "The Sharks and the Soles" coupled diff. equations. I suggest Antti introduce that model to the little genius.

bc, barely can do that one.

Monsieur et Madame Vieuxbouc wrote:

Is this a mathematical exercise or does the student want to consider practical solutions as well. Many have already commented on a purely mathematical approach, but in reality, there are a great many number of limiting factors to affect the growth curve. Living organisms do not follow a mathematical model indefinitely. In the lab, the growth rate depends on the volume of the container, the addition of nutrients, the subtraction of wastes. With little outside involvement, you would soon see an *S* curve an then a collapse, down to a very low sustainable level or even to zero eventually. In nature continued growth would also depend on the host if it is a disease germ, and you must consider immune factors kicking in, and other bodily functions to contain the infection, again the growth levels off to zero growth and eventually a drop almost to zero. If it were in a pond or other natural environment other factors include temperature, nutrients in the environment, pH of the water supply, and a host of other considerations (including smaller *bugs* feasting off the germ, so you might be able to see a microfood chain taking place given time and proper equipment to observe such events).
As part of a graduate school project in microbiology we did a study of yeast colonies under differing controlled conditions where we added and subtracted various nutrients and waste by-products and a number of other factors in the dishes and did counts of the growth patterns. That was many, many years ago, so I mostly had forgotten this until this question came up.
If this student just wants to model a pure mathematical growth curve as in a simple *what-if* computer game, well, forget everything I wrote. But, if the student is interested in what really happens, then there are all these considerations and more which fall well outside the realm of the *pure* models.

Marty








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