## Colorado (R

## Ohio (R_{t})

## The numbers behind social distancing

## The effective reproduction number in time-dependent epidemic trends

## Abstract

Although the basic reproduction number, *R* _{0}, is useful for understanding the transmissibility of a disease and designing various intervention strategies, the classic threshold quantity theoretically assumes that the epidemic first occurs in a fully susceptible population, and hence, *R* _{0} is essentially a mathematically defined quantity. In many instances, it is of practical importance to evaluate time-dependent variations in the transmission potential of infectious diseases.

Explanation of the time course of an epidemic can be partly achieved by estimating the effective reproduction number, *R(t)*, defined as the actual average number of secondary cases per primary case at calendar time *t* (for *t >*0). *R(t)* shows time-dependent variation due to the decline in susceptible individuals (intrinsic factors) and the implementation of control measures (extrinsic factors). If *R(t)*<1, it suggests that the epidemic is in decline and may be regarded as being *under control* at time *t*.

**SOURCE:** Hiroshi + Chowell