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For K-12 Students · SIR Epidemic

SIR Epidemic for a circadian rhythm

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a circadian rhythm live below — adjust the inputs and watch it respond, right in your browser.

SIR Epidemic ModelLive

compartmental disease dynamics

Controls

Presets

Basic reproduction R₀

Infectious period (days)

Initial immune (vaccinated)

The SIR model splits a population into Susceptible, Infected, and Recovered and lets them flow between compartments. R₀ — the average number infected by one case — sets whether an outbreak grows. Vaccinating above the herd-immunity threshold 1−1/R₀ prevents an epidemic outright.

▶ Run in Python

Data Inspector

Peak infected0.0%

Total infected0.0%

Herd immunity60%

Governing equation

\frac{d S}{d t} = - β S I, \frac{d I}{d t} = β S I - γ I, \frac{d R}{d t} = γ I; β = 0.357, γ = 0.143, R_{0} = \frac{β}{γ} = 2.50

Reading this result: R₀ = 2.50 > 1 with only 0% immune, so infections grow into an epidemic. You would need to immunize 60% (the herd-immunity threshold 1−1/R₀) to stop it; the current effective reproduction number is 2.50.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "SIR Epidemic for a circadian rhythm" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.