= Solution
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> is
$$
\Delta_t=\sum_{\tau=1}^{t}\beta_{t,\tau}\Delta_{t-\tau},
$$
up 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.
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