Epidemiology & Public Health

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

Epidemiology & Public Health formulas help you understand how diseases spread, how outbreaks are measured, and how population health is tracked. From incidence and prevalence to reproduction numbers, SIR models, and risk metrics like relative risk and odds ratio, these tools are essential for students, exam revision, and real-world work in medicine, public health, and research.

Incidence Rate

IR = \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.

Prevalence

P = \frac{\text{Existing Cases}}{\text{Total Population}} \times k

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

Basic Reproduction Number

NEWIntermediate

R_0 = \beta \times D

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

Herd-Immunity Threshold

NEWIntermediate

H = 1 - \frac{1}{R_0}

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

Effective Reproduction Number

NEWIntermediate

R_e = R_0 \times S

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

SIR Model — Susceptible

\frac{dS}{dt} = -\beta S I

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

SIR Model — Infected

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

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

SIR Model — Recovered

\frac{dR}{dt} = \gamma I

Rate at which infected individuals recover and gain immunity.

Case Fatality Rate

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

Proportion of diagnosed individuals who die from the disease.

Attack Rate

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

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

Relative Risk

NEWIntermediate

RR = \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.

Odds Ratio

NEWIntermediate

OR = \frac{a \times d}{b \times c}

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

Number Needed to Treat

NEWIntermediate

NNT = \frac{1}{ARR}

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