Disease spread and herd immunity (SIR model)
BiologyHealth & DiseaseAges 16–17
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Health & Disease
The SIR model divides a community into susceptible, infected, and recovered groups. Choose a disease (seasonal flu, COVID-19, measles) with a realistic basic reproduction number R₀, then adjust the vaccination rate and the contact-reduction level (masks, distancing, isolation) to see the epidemic peak drop, arrive later, and the total case count fall – and once the herd-immunity threshold 1 − 1/R₀ is passed, the outbreak cannot take off.
Lesson: Human epidemics and how to prevent and control them
What it shows
The SIR model splits a population into susceptible, infected and recovered people and follows how individuals move between the groups each day. The effective reproduction number Rₑ = R₀(1 − c)(1 − v·e) combines the disease's basic reproduction number with contact reduction c, vaccination coverage v and vaccine efficacy e. When Rₑ falls below 1, each case infects fewer than one other person and the outbreak dies out. The herd-immunity threshold 1 − 1/R₀ explains why measles needs far higher coverage than seasonal flu.
How to use
Pick a Disease and leave vaccination and contact reduction at zero to see an unchecked outbreak, noting the peak day, the peak size and whether the curve crosses the hospital capacity line. Then raise Vaccination step by step until the outbreak no longer takes off and compare that value with the threshold shown. Repeat using Contact reduction alone, and drag the Day slider to follow the dot grid through the epidemic.
Parameters you can change
- Disease Seasonal flu (R₀ ≈ 1.5), COVID-19 original strain (R₀ ≈ 3), Measles (R₀ ≈ 15)
- Share of population vaccinated 0–99 %
- Contact reduction level 0–90 %
Questions to explore
- Why does measles need a much higher vaccination rate than seasonal flu to prevent an outbreak?
- What does a lower epidemic peak change for hospitals, and why does that matter?
- Which quantity in the model does wearing masks change, and how does that affect Rₑ?
