Incubation Exposure Bounds

Derive interval-censored incubation bounds from exposure windows and symptom onsets.

Description

Translate aligned exposure windows and symptom-onset times into minimum and maximum possible incubation durations.

An incubation period runs from infection to symptom onset. Infection time is often unobserved, while a history may identify an interval during which exposure could have occurred. Such records provide bounded durations rather than an exact incubation time.^[1]

For onset on day 7 after possible exposure from day 0 through day 2, the shortest duration is 7−2 = 5 days and the longest is 7−0 = 7 days. These arithmetic bounds assume the relevant infection occurred within the supplied exposure window.

Incubation Exposure Bounds returns paired duration lists in input order. It does not choose an infection time within each window or fit a population incubation distribution.

When to summarize uncertain exposure timing

Use this tool for records with a defined earliest exposure, latest exposure, and onset on a shared day axis. It preserves timing uncertainty instead of substituting the midpoint of an exposure interval.

Prepare lower and upper duration bounds for each record.
Check ordering of exposure windows relative to onset.
Separate timing bounds from statistical confidence intervals.

How to enter exposure windows and calculate incubation bounds

Enter nonempty aligned Earliest exposure days, Latest exposure days, and Onset days lists.
For each record, ensure earliest exposure ≤ latest exposure ≤ onset.
Use consistent elapsed-day coordinates, including fractional days when needed.
Run the tool and pair each Minimum incubation days and Maximum incubation days entry with its source record.

minimum_i = onset_i − latestExposure_i; maximum_i = onset_i − earliestExposure_i

Subtracting the latest possible exposure gives the shorter duration. The tool checks ordering within each record, not chronological sorting of records across the list.

json

{
  "input": {
    "earliestExposureDays": [
      0,
      1
    ],
    "latestExposureDays": [
      2,
      3
    ],
    "onsetDays": [
      7,
      9
    ]
  },
  "output": {
    "minimumIncubationDays": [
      5,
      6
    ],
    "maximumIncubationDays": [
      7,
      8
    ]
  }
}

Coincident earliest and latest times produce an exact point duration. Latest exposure equal to onset gives a zero minimum. Negative coordinate values are accepted when ordered; they can represent dates before the chosen origin. Empty/misaligned lists, incompatible ordering, or nonfinite inputs produce errors.

Limitations and interpretation

The bounds depend on the supplied exposure history and do not prove that transmission occurred in that interval.
No incubation quantile, distribution fit, midpoint estimate, censoring likelihood, or uncertainty interval is computed.
Symptom-onset uncertainty is not modeled separately; onset is treated as a supplied point time.
Incubation describes symptom timing and is distinct from the latent period to infectiousness or a laboratory detection window.

Alternative or Complementary methods

Retain the original exposure intervals for any interval-censored statistical analysis. Infection/onset transmission pairs can compare generation and serial intervals, while a supplied quarantine-window calculation uses an externally chosen duration.

References

The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application — Annals of Internal Medicine; S. A. Lauer and colleagues (2020)

Similar or alternative tools

Generation Serial Interval Pairs
Compare supplied infection-to-infection and onset-to-onset timing in transmission pairs.
Exposure Quarantine Window
Add a supplied incubation-duration quantile and buffer to a last-exposure time.