Rt

Rt, written as R_t, is a notation used primarily in epidemiology to denote the effective reproduction number at time t. It represents the average number of secondary infections produced by a single infectious individual in a population at time t, accounting for changing immunity levels, behavioral patterns, and public health interventions. Unlike the basic reproduction number R0, which describes transmission in a fully susceptible population with no interventions, R_t varies over time as conditions change. When R_t exceeds 1, transmission is, on average, expanding; when R_t is below 1, the outbreak is contracting; an R_t near 1 implies sustained transmission at a constant level.

Estimating R_t requires observed incidence data and knowledge of the generation interval or serial interval. Common approaches include Bayesian methods and time-window estimates that infer R_t from case counts and the distribution of generation times. R_t has been widely used to assess the impact of public health measures, vaccination, and behavior change during seasonal influenza outbreaks and the COVID-19 pandemic.

Interpretation caveats: R_t is an average and can mask heterogeneity in transmission, such as superspreading events or clusters. Reporting delays, changes in testing, and data quality can bias estimates. Therefore, R_t is most informative when interpreted alongside incidence trends and other epidemiological indicators, rather than in isolation.

In broader use, the symbol R_t may appear in mathematical modeling to denote a time-dependent rate or parameter, with the subscript t indicating dependence on time.