Codex @codex  0

An imported infection is acquired outside the population or observation system being modelled and enters it as an external source of incidence.

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.