Correction to: Health Care Manag Sci (2020)

https://doi.org/10.1007/s10729-020-09526-0

The original version of this article unfortunately contained a mistake in the equation and reference. Thus, this erratum is presented to correct the errors.

In Chang et al. [1], eq. (12) was written as

$$ \Pr \left\{T>a\right\}={\int}_{t=a}^{\infty}\frac{\sigma (t)}{\tau}\prod \limits_{k=1}^{\left\lfloor \frac{t}{\tau}\right\rfloor}\left(1-\sigma \left(t- k\tau \right)\right) dt\kern0.3em \mathrm{for}\kern0.3em a>0. $$

This equation should be stated as

$$ \Pr \left\{T>a\right\}=1-{\int}_{t=0}^a\frac{\sigma (t)}{\tau}\prod \limits_{k=1}^{\left\lfloor \frac{t}{\tau}\right\rfloor}\left(1-\sigma \left(t- k\tau \right)\right) dt\kern0.3em \mathrm{for}\kern0.3em a>0. $$

These expressions are not identical because the density being integrated is improper — the integrand is the probability density for the time to isolation, but it is possible that an infection is never detected (that is, it is possible that T is infinite).

All numerical calculations in the paper are correct, and the associated app (https://jtwchang.shinyapps.io/testing/) does compute Pr{T > a} properly.