Epidemiology & Public Health
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SIR Model — Recovered

Rate at which infected individuals recover and gain immunity.

Formula

dRdt=γI\frac{dR}{dt} = \gamma I

Variables

RRecovered fraction
IInfected fraction
\gammaRecovery rate
tTime

Example

γ = 0.1, I = 0.1 → dR/dt = 0.01

Did You Know?

In the SIR model, S + I + R = 1 always — every person is in exactly one compartment at any moment.

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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 — Susceptible

Advanced

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