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Epidemiology & Public Health

Disease-spread models, outbreak metrics and population-health measures

Incidence Rate

NEWBasic
IR=New CasesPopulation at Risk×kIR = \frac{\text{New Cases}}{\text{Population at Risk}} \times k

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

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Prevalence

NEWBasic
P=Existing CasesTotal Population×kP = \frac{\text{Existing Cases}}{\text{Total Population}} \times k

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

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Basic Reproduction Number

NEWIntermediate
R0=β×DR_0 = \beta \times D

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

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Herd-Immunity Threshold

NEWIntermediate
H=11R0H = 1 - \frac{1}{R_0}

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

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Effective Reproduction Number

NEWIntermediate
Re=R0×SR_e = R_0 \times S

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

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SIR Model — Susceptible

NEWAdvanced
dSdt=βSI\frac{dS}{dt} = -\beta S I

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

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SIR Model — Infected

NEWAdvanced
dIdt=βSIγI\frac{dI}{dt} = \beta S I - \gamma I

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

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SIR Model — Recovered

NEWAdvanced
dRdt=γI\frac{dR}{dt} = \gamma I

Rate at which infected individuals recover and gain immunity.

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Case Fatality Rate

NEWBasic
CFR=DeathsConfirmed Cases×100CFR = \frac{\text{Deaths}}{\text{Confirmed Cases}} \times 100

Proportion of diagnosed individuals who die from the disease.

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Attack Rate

NEWBasic
AR=Cases during outbreakPopulation exposed×100AR = \frac{\text{Cases during outbreak}}{\text{Population exposed}} \times 100

Proportion of an exposed population that develops the illness during an outbreak.

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Relative Risk

NEWIntermediate
RR=Risk in ExposedRisk in UnexposedRR = \frac{\text{Risk in Exposed}}{\text{Risk in Unexposed}}

How many times more likely the exposed group is to develop the disease compared to the unexposed group.

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Odds Ratio

NEWIntermediate
OR=a×db×cOR = \frac{a \times d}{b \times c}

Ratio of the odds of exposure among cases versus controls in a case-control study.

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Number Needed to Treat

NEWIntermediate
NNT=1ARRNNT = \frac{1}{ARR}

Number of patients who must receive a treatment for one additional patient to benefit.

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