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.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 207 / 2 / f / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-207/2/f/solution