# How to make mathematical models (even at home)

As a WordPress blogger, I get a handy list of search terms that have led people to my blog. A particularly memorable search term that showed up on my feed was ‘how to make mathematical models at home’. What I liked about this query was that it suggests mathematical modelling as a recreational hobby: at home, in one’s spare time; just for fun. This speaks to an under-appreciated quality of mathematical modelling – that it’s really quite accessible once the core principles have been mastered.

To get started, I would suggest any of the following textbooks*:

Now, I know, you want to make your own mathematical model, not just read about other people’s mathematical models in a textbook. To start down this road, I think you should pay attention to two things:

• How to make a diagram that represents your understanding of how the quantities you want to model change and interact, and;
• Developing a basic knowledge of the classic models in the ecology, evolution and epidemiology including developing an understanding of what these models assume.

This would correspond to reading Chapters 2 and 3 of A Biologist’s Guide to Mathematical Modeling.

Remember that the classic model usually represents the most simple model that will be appropriate, and only in rare circumstances, might you be able to justify using a more simple model. For example, if the level of predation or disease spread for your population of interest is very low, then you might be able to use a model for single species population growth (exponential/logistic/Ricker) instead of the Lotka-Volterra or SIR models, however, if predation and disease spread are negligible, then it arguably wasn’t appropriate to call your problem ‘predator-prey’ or ‘disease spread’ in the first place. Almost by definition, it’s usually not possible to go much simpler than the dynamics represented by the appropriate classic model.

That should get you started. You can do this at the university library. You can do this for a project for a class. And, yes, you can even do this at home!

Footnotes:

*For someone with a background in mathematics some excellent textbooks are:

but while the above textbooks will give you a better understanding of how to perform model analysis, the ‘For Biologist’s’ textbooks listed in this post are still the recommended reading to learn about model derivation and interpretation.

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