IA idea · Differential equations & dynamics

How fast would flu spread through my school? An SIR model

AI HLAA HL Ambitious Also in: Health & biology, Statistics

Research question

How do the infection and recovery rates in an SIR model affect the peak number of students ill at once in a school of my school's size, and what vaccination level would keep the peak below 5%?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

The SIR model became famous during COVID-19. Building one for your own school, solving it with Euler's method, and asking what vaccination level prevents a big outbreak is serious applied mathematics with a clear decision at the end.

The mathematics you'll need

Coupled differential equations dS/dt, dI/dt, dR/dt
Euler's method in a spreadsheet; effect of step size
The basic reproduction number R₀ = β/γ
Sensitivity analysis on parameters
Herd-immunity threshold 1 − 1/R₀

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Use published values of R₀ and infectious period for influenza from public-health sources; optionally compare with anonymised absence counts from your school (with permission).

WHO Global Health Observatory — 1,000+ health indicators by country (immunisation, mortality, risk factors).
Our World in Data — Clean country-level time series (CO₂, population, health, energy, education) with CSV download on every chart.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain the compartments and the assumptions (well-mixed population).
Choose and justify parameters.
Solve numerically and find the peak.
Vary vaccination levels to find the threshold.
Reflect: schools are not well mixed; weekends and classes matter.

Pitfalls that cost marks

Parameters with no source.
Euler's method with a step too large, giving negative numbers.
Presenting the model as a prediction for your real school.

Showing personal engagement

Model your own school's size and structure.
Split the school into year groups with different mixing.
Compare the model with a real outbreak in the news.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Add a latent (Exposed) compartment for an SEIR model and compare peak timing.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).