Skip to content
Medical Sciences
Epidemiology
1927
Intermediate

SIR Model

dSdt=−βSI,dIdt=βSI−γI,dRdt=γI\frac{dS}{dt} = -\beta SI, \quad \frac{dI}{dt} = \beta SI - \gamma I, \quad \frac{dR}{dt} = \gamma I

Susceptible become Infected at rate βSI; Infected Recover at rate γI.

By W.O. Kermack, A.G. McKendrick

Medical Sciences
SIR Model
1927 · W.O. Kermack
Classroom Ready
89%

Rabbit Hole Mode

Five doors into the universe behind this equation. Choose your path.

Story PortalWho discovered this?Discover how Kermack and McKendrick and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — public health forecasting systems.Math PortalWhat does it derive from?Trace the mathematical lineage from exponential growth and decay.Future PortalWhere is it going?Network and behavioral extensions
Launch collection — full story, visual, sound & share card
Why it matters: Foundation of epidemiology—used for COVID-19, flu, and vaccination policy.

Discoverers: W.O. Kermack, A.G. McKendrick (1927)

What does it mean?

Susceptible become Infected at rate βSI; Infected Recover at rate γI.

Why should I care?

Foundation of epidemiology—used for COVID-19, flu, and vaccination policy.

Equation Compass

North — Prerequisites

West — History

East — Applications

South — Derivations

Variables & Units

SymbolNameUnitMeaning
SSSusceptible—Fraction susceptible
IIInfected—Fraction infected
RRRecovered—Fraction recovered
ββTransmission—Infection rate
γγRecovery rate—1/infectious period

Worked Example

R₀ = β/γ; R₀ > 1 → epidemic grows.

AI Guide (Pro)

Ask questions about equations and get answers grounded in the Equation Universe catalog.

Upgrade to ProTry demo (7 days)

Continue your trail

MedicineBiomedical EngineerSI

Sources & further reading

Search WikipediaSearch Wolfram MathWorldOpen in Wolfram|AlphaWatch explainers on YouTube

Share this equation

Equation Universe

SIR Model

dSdt=−βSI,dIdt=βSI−γI,dRdt=γI\frac{dS}{dt} = -\beta SI, \quad \frac{dI}{dt} = \beta SI - \gamma I, \quad \frac{dR}{dt} = \gamma I

Real-world impact

Pandemic forecasting

Compartment models guide public-health policy and vaccine rollout.

Photo: Unsplash — medical research

Susceptible become Infected at rate βSI; Infected Recover at rate γI.

equation-universe.vercel.app

Post