Solution
= Solution
Hospital admissions are a delayed thinning of infections. If $f(s)$ is the delay density and $\lambda(t)$ denotes the population infection incidence rate, then the <convolution>
$$
\mu(t)=p\int_0^t\lambda(t-s)f(s)\,ds
=p\int_0^tf(t-s)\lambda(s)\,ds
$$
is the admission incidence rate, with an additional term for infections before time zero if the observation window starts during an epidemic.