= Solution
Let $u$ be the infection time and $s=t-u\geq0$ its incubation delay, with independent delays having <probability density function> $f(s)$. Each infection contributes to the symptom-onset intensity according to its delay density. <Back-calculation of infection incidence> uses the <convolution>
$$
\boxed{\mu(t)=\int_{-\infty}^{t}h(u)f(t-u)\,du
=\int_0^\infty h(t-s)f(s)\,ds.}
$$
\b[Observed onset intensity is infection intensity convolved with the incubation distribution.] If infections begin at a known $t_0$, take $h(u)=0$ for $u<t_0$, reducing the first integral's lower limit to $t_0$. Otherwise past infections must be included; the observation window's start need not be the infection process's start.
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