Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

How much vaccination is enough to stop measles?

AI SLAI HLAA SL Solid Also in: Statistics, Differential equations

Research question

Across countries, how is measles incidence related to vaccination coverage, and is there evidence of a threshold near the herd-immunity level predicted by R₀?

Make it yours, then agree it with your teacher.

Next step: plan this IA free — the planner opens with this question filled in. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.

Why it makes a good exploration

Measles is extremely contagious, so its herd-immunity threshold is very high. Comparing WHO data with the simple formula 1 − 1/R₀ links statistics with epidemic modelling.

The mathematics you'll need

Scatter plots with log-scaled incidence
Correlation and regression
Herd immunity threshold 1 − 1/R₀
Piecewise or threshold models

Modelling the data, step by step

This idea usually needs a piecewise model. See it worked step by step, with a criterion tip at every step: Piecewise models.

Model your own data Paste it from Desmos, GeoGebra or a spreadsheet and get the same play-by-play with your numbers. New to modelling? Start with the modelling workflow. Writing it up? The IA modelling planner comments on each paragraph as you draft — it never writes it for you.

Where the data comes from

Coverage and reported cases by country and year from the WHO Global Health Observatory.

WHO Global Health Observatory — 1,000+ health indicators by country (immunisation, mortality, risk factors).

Real data for this idea

Primary source: World Bank Open Data: Immunisation, measles (SH.IMM.MEAS). Percentage of children aged 12–23 months vaccinated, by country and year. Licence: CC BY 4.0 for most datasets (the World Bank's licence page lists any exceptions).
Also useful: WHO Global Health Observatory: WHO immunisation data portal. Use the measles reported-cases and coverage tables for the countries you choose. Licence: CC BY-NC-SA 3.0 IGO: non-commercial use only, credit WHO, share alike.
Readable chart: Our World in Data: Share of one-year-olds vaccinated against measles. Use it to see the pattern; download your numbers from the primary source or the chart's own download. Cite as: Our World in Data, ‘Share of one-year-olds vaccinated against measles’, CC BY 4.0. Original source: WHO & UNICEF (2026); UN, World Population Prospects (2024).
Readable chart: Our World in Data: Reported cases of measles. Use it to see the pattern; download your numbers from the primary source or the chart's own download. Cite as: Our World in Data, ‘Reported cases of measles’, CC BY 4.0. Original source: World Health Organization, Global Health Observatory (2026).

Coverage for recent years is partly estimated: say which years are reported and which are estimates. WHO data is licensed for non-commercial use only (CC BY-NC-SA 3.0 IGO): fine for a school project, and credit WHO. Links checked October 2026; we link to the data and never copy it. More free data sets.

A possible outline

Explain R₀ and herd immunity.
Plot incidence against coverage.
Model the relationship; test for a threshold.
Compare with the theoretical threshold.
Reflect on under-reporting, clustering and imported cases.

Pitfalls that cost marks

Treating countries as one population.
Ignoring reporting quality.
Logs of zero incidence.

Showing personal engagement

Look at your own country's history of outbreaks.
Explain clustering of unvaccinated groups.
Discuss the ethics of using this data carefully.

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

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Scatter plots with log-scaled incidence; Correlation and regression
AA HL	Not a natural fit	The mathematics is mainly from the AI course; at AA HL the exploration would need an AA-level approach (calculus, proof or probability theory) to reach the top of Criterion E.
AI SL	Good fit	Scatter plots with log-scaled incidence; Correlation and regression
AI HL	Good fit	Scatter plots with log-scaled incidence; Correlation and regression

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: treating countries as one population; and ignoring reporting quality. Say how each one affects your answer.

Use of mathematics (E)

SL: scatter plots with log-scaled incidence; correlation and regression; herd immunity threshold 1 − 1/R₀; piecewise or threshold models, each explained in your own words and carried out correctly.

How health & biology explorations reach the top bands in general: Health, biology & medicine IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Simulate an SIR model with vaccination and compare outbreak sizes around the threshold.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL health & biology exploration adds.

See a complete IA, marked

Is it cheaper to leave the heating on low overnight? A two-temperature model of my bedroom (AI HL) is a complete health & biology exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI SL, AI HL and AA SL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Scatter plots with log-scaled incidence, correlation and regression, herd immunity threshold 1 − 1/R₀ and piecewise or threshold models.

Where can I get data for this IA?

Coverage and reported cases by country and year from the WHO Global Health Observatory. Checked sources and tools: World Bank Open Data, WHO Global Health Observatory and Our World in Data.

Turn this idea into your IA

The planner opens with “How much vaccination is enough to stop measles?” filled in: the question, the maths and the data sources.

Plan this IA free

Your plan is kept in this browser. A free account keeps it with your drafts on any device: Join free · Sign in

Also: free IA self-check · A–E checklist (PDF) · have a draft? AI feedback or a review with Pete (€100)

Writing it up: how to write a Maths IA, step by step · structure and format · mistakes that cost marks · IA statistics, step by step