Maths in biology and medicine · Ambitious · Dissertation

Models of tumour growth: a maths EPQ idea

Why it works as an EPQ

Three models, one published data set, and a fair method of choosing between them.

Scope and difficulty

Ambitious. Ambitious. Published data only; no medical claims.

The maths

Builds on these A Level topics: Exponentials and logarithms · Differentiation · Numerical methods.

You would learn:

• The Gompertz model
• Least squares fitting
• Comparing models fairly

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Derive each model from its assumptions.
2. Fit each to published data.
3. Compare them with a fair criterion and on held-back data.
4. Judge which is best and for what purpose.

Pitfalls

• Choosing the model with most parameters because it fits best.
• Medical claims.

Where to start reading

• Search for: Gompertz tumour growth model
• Search for: comparing models held out data overfitting

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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All maths in biology and medicine ideas · all 93 ideas

Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.