Epidemiology & Public Health
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SIR Model — Susceptible

Rate of change of the susceptible population in the SIR compartmental model.

Formula

dSdt=−βSI\frac{dS}{dt} = -\beta S I

Variables

SSusceptible fraction
IInfected fraction
\betaTransmission rate
tTime

Example

β = 0.3, S = 0.9, I = 0.1 → dS/dt = −0.027

Did You Know?

The SIR model was first published by Kermack and McKendrick in 1927 and is still the foundation of modern epidemic modelling.

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Incidence Rate

Basic

Rate at which new cases of a disease appear in a population over a given period.

Prevalence

Basic

Proportion of a population that has a particular condition at a point in time.

Basic Reproduction Number

Intermediate

Average number of secondary infections produced by one infected individual in a fully susceptible population.

Herd-Immunity Threshold

Intermediate

Minimum fraction of the population that must be immune to prevent sustained spread.

Effective Reproduction Number

Intermediate

Actual average infections per case when part of the population is already immune.

SIR Model — Infected

Advanced

Rate of change of the infected population — new infections minus recoveries.