The model that shaped how the world thinks about outbreaks. Watch susceptible, infected, and recovered populations flow through an epidemic, and see how R₀ and vaccination change everything.
SIR Epidemic ModelLive
compartmental disease dynamics
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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.
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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How it works
The SIR model divides a population into Susceptible, Infected, and Recovered compartments linked by differential equations. The basic reproduction number R₀ decides whether an outbreak grows or fizzles, and vaccinating above the herd-immunity threshold 1−1/R₀ stops it before it starts. A conceptual epidemiological model for education.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Yes. SIR Epidemic Model runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
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Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.