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Calendar time locates an event on a shared external timeline, in contrast with an individual's age or the time elapsed since an individual event.

The instantaneous reproduction number freezes the transmission conditions at calendar time $t$ and counts the expected secondary infections produced over a complete infectious lifetime under those conditions.

The first subscript in ${\beta }_{t,\tau }$ is the calendar time $t$, and the second is the infection age $\tau$, the time elapsed since the source individual became infected. Thus ${\beta }_{t,\tau }$ is the rate at which an individual of infection age $\tau$ generates infections at time $t$. The corresponding discrete infectious disease renewal equation isup to a separately modelled term for imported infection. The upper limit may instead be a fixed maximal infectious age, with unavailable terms set to zero.

A time-varying reproduction number describes transmission at a specified calendar time while allowing transmission conditions to change during an epidemic.