Modelling an epidemic: a maths EPQ idea
A title to start from
How well does a simple SIR model capture the spread of an epidemic, and what does it imply for vaccination?
Why it works as an EPQ
Three differential equations, solved numerically, give a herd-immunity threshold you can derive and test.
Scope and difficulty
Solid. Solid. Model, solve, compare with one published outbreak.
The maths
Builds on these A Level topics: Differentiation · Numerical methods · Exponentials and logarithms.
You would learn:
- Systems of differential equations
- The basic reproduction number R₀
- Herd-immunity threshold 1 − 1/R₀
One possible plan
- Set up the SIR equations and explain each term.
- Solve numerically and explore R₀.
- Derive the herd-immunity threshold.
- Compare with a documented outbreak and judge the model's limits.
Pitfalls
- Health advice beyond the model.
- Real data used without understanding how it was collected.
Where to start reading
- Search for: SIR model R0 herd immunity threshold derivation
- Mathematical Biology (J. D. Murray), the epidemics chapter
Similar ideas
- When a positive test is probably wrongWhy can a positive result from an accurate medical test still be more likely wrong than right?
- Planning repeated drug dosesHow do exponential decay and geometric series explain the dosing of repeated medicines?
- Predator and prey cyclesCan the Lotka–Volterra equations explain the cycles in predator and prey populations?
- How big should a clinical trial be?How many patients does a clinical trial need for enough statistical power, and what goes wrong when it is too small?
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.