But what is Mathematical Biology?

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Differential Equations

If you're not sure what a differential equation is, here's an explanation.

Mathematical Models

When biologists do experiments, they measure quantities such as cell density (number of cells in a certain volume) and chemical concentration (amount of chemical in a certain volume). Mathematical biologists use their knowledge of biological processes to make up differential equations which will hopefully describe how these quantities change with time. Each term in the differential equation describes a process that would affect the number of cells or amount of chemical, etc.

For instance, if I was trying to describe how the number of fibroblast cells in your skin changes with time, I might write c for the number of cells per cubic centimeter. The left hand side of the equation would be

                         dc
                         --
                         dt

to show that I'm describing how c changes over time, t, and the right-hand side would include a term like

                      c (C - c)

to show that when the number of cells is less than the normal healthy level, C, the cells will begin reproducing themselves, and when it is higher than C, then the extra ones will begin to die off.

A mathematical model is just a differential equation, or set of differential equations, that describe some process. The process could be biological (like the fibroblast reproduction and death described above), or it could be physical (like Newton's Second Law) or even financial.

What's the Point?

If I make a mathematical model of some biological process, as mentioned above, each term in it should mean something. When I use a computer to solve my equations, I can compare my results with experimental data. If they agree, it usually means that I have included all the important biological things that combine to give the observed result. If they disagree, I have missed something out, or put something in that doesn't actually happen.

For instance, the fibroblast model above wouldn't describe the behaviour of fibroblasts in wounded skin very well, because I haven't put in a term to show that they tend to move towards a wound to help heal it.

So a mathematical model can help biologists to find out what is really happening when a wound heals. It can help guide them towards experiments which could be useful, and away from experiments which probably wouldn't tell them much.

Mathematical modelling is an alternative to animal testing!



29 August 1997