Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 207 / 2 / f / 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 convolutionis the admission incidence rate, with an additional term for infections before time zero if the observation window starts during an epidemic.