Epidemiology & Public Health
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SIR Model — Infected

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

Formula

dIdt=βSI−γI\frac{dI}{dt} = \beta S I - \gamma I

Variables

IInfected fraction
SSusceptible fraction
\betaTransmission rate
\gammaRecovery rate (1/D)
tTime

Example

β=0.3, S=0.9, I=0.1, γ=0.1 → dI/dt = 0.027 − 0.01 = 0.017

Did You Know?

The peak of I — the tallest point of the epidemic curve — is what 'flatten the curve' campaigns try to lower.

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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.