r0

R0, or basic reproduction number, is an epidemiology concept that expresses the average number of secondary infections caused by a single infectious individual in a population that is entirely susceptible and in which no interventions are in place. It is used to describe the potential for spread at the start of an outbreak.

R0 is not a fixed property of a pathogen; it depends on factors including the biology of the pathogen, the mode of transmission, contact patterns within the population, and the duration of infectiousness. In mathematical terms, it can be approximated as R0 ≈ β c D, where β is transmission probability per contact, c is contact rate, and D is duration of infectiousness; in other models R0 may be expressed as the product of these factors.

Interpretation and thresholds: If R0 > 1 the outbreak can grow in a completely susceptible population; if R0 < 1 the outbreak will tend to die out. The herd immunity threshold is 1 − 1/R0, representing the proportion of the population that must be immune to halt sustained transmission, assuming homogeneous mixing.

Examples: Measles typically has a high R0, often estimated around 12–18; seasonal influenza around 1.3–1.8, and SARS-CoV-2 early in the pandemic around 2–3, though estimates vary by variant and context.

Relation to Rt: Rt or R(t) is the effective reproduction number at time t, reflecting immunity in the population and control measures. R0 is the initial value in a fully susceptible population without interventions.

Limitations: R0 assumes homogeneous mixing and no preexisting immunity; real populations exhibit heterogeneity, clustering, and super-spreading, which can cause deviations. Estimation is sensitive to data quality and model assumptions.