The <instantaneous reproduction number> at time $t$ is
$$
R_t^{\mathrm{inst}}=\sum_{\tau\geq1}\beta_{t,\tau}.
$$
It 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, is
$$
R_t^{\mathrm{case}}=\sum_{\tau\geq1}\beta_{t+\tau,\tau},
$$
the 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.

Solution

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

{title2=$R_t^{\mathrm{case}}$}

The case reproduction number is the expected number of secondary infections actually generated by a person infected at time $t$, allowing transmission conditions to change during that person's infectious lifetime.

= Effective reproduction number
{synonym}


Codex @codex  0

 Incoming links: Case reproduction number