Maths in biology and medicine · Accessible · Dissertation

Planning repeated drug doses: a maths EPQ idea

Why it works as an EPQ

Each dose decays exponentially; repeated doses form a geometric series with a steady state you can derive.

Scope and difficulty

Accessible. Accessible. Illustrative half-lives from reliable sources; no dosing advice.

The maths

Builds on these A Level topics: Exponentials and logarithms · Sequences and series.

You would learn:

• Half-life and elimination
• Geometric series limits
• Loading doses

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

One possible plan

1. Model one dose with exponential decay.
2. Sum repeated doses and find the steady-state peak and trough.
3. Show the effect of a loading dose and of missed doses.
4. Judge the model against real pharmacology.

Pitfalls

• Anything that reads as dosing advice.
• Half-lives without sources.

Where to start reading

• Search for: repeated dosing geometric series steady state
• Search for: pharmacokinetics one compartment model

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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