Attack Rate

Gist

An attack rate is the proportion of the population at risk that got infected. Note that it's not a rate, it's a proportion! TLDR: The cumulative incidence of disease during an outbreak.

Formula

A R = \frac{T o t a l I n f e c t i o n s}{N}

where we accumulate the total incidence (getting total infections) and dividing it over $N$ , the population at risk.

Relation to

Reproductive number (From Kretzschmar and Wallinga 2009) :
$$
AR = (1- exp(-R\times AR)),
$$
where $R$ is the reproductive number.

Usage

Needed for calculating Vaccine efficacy

Clinical trials

A way to do case projections.

References

Kretzschmar, Mirjam, and Jacco Wallinga. "Mathematical models in infectious disease epidemiology." Modern infectious disease epidemiology: Concepts, methods, mathematical models, and public health. New York, NY: Springer New York, 2009. 209-221.

Billard, Marie-Noëlle, et al. "Year-to-year variation in attack rates could result in underpowered respiratory syncytial virus vaccine efficacy trials." Journal of Clinical Epidemiology 147 (2022): 11-20.