Infectivity profile

An infectivity profile describes how an infected individual's transmission rate varies with infection age.

The generation interval is the time between infection of a source individual and infection of a secondary case caused by that source.

The generation-interval distribution gives the probability law of the generation interval. In discrete time, its probabilities $g_{\tau }$ form a nonnegative sequence summing to one.

The infectious disease renewal equation expresses current incidence as a convolution of past incidence with an infectivity profile, multiplied by a time-varying transmission level.

For incidence $I_t$ and discrete generation-interval probabilities $g_{\tau }$, the total infectiousness at time $t$ is ${\Lambda }_t={\sum }_{\tau \ge 1}{g}_{\tau }{I}_{t-\tau }$.

A time-varying reproduction number describes transmission at a specified calendar time while allowing transmission conditions to change during an epidemic.

The instantaneous reproduction number freezes the transmission conditions at calendar time $t$ and counts the expected secondary infections produced over a complete infectious lifetime under those conditions.

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.