Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 1 / b / i

The instantaneous reproduction number at time $t$ isIt is the expected number of secondary infections that one infected individual would produce if the transmission conditions at time $t$ applied throughout that individual's infectious life. The case reproduction number, also called the effective reproduction number in this question, isthe expected number actually produced by a person infected at $t$ as calendar-time conditions subsequently change. The instantaneous quantity is easier to estimate in real time because it depends on current and past incidence; the case quantity depends on future conditions.