Generation Serial Interval Pairs

Derive paired infection-to-infection and onset-to-onset intervals, retaining possible negative serial intervals.

Description

Compare infection-to-infection and onset-to-onset intervals in transmission pairs, retaining signed serial intervals and their mean difference.

A generation interval measures time from a source infection to its recipient infection. A serial interval measures time between their symptom onsets. The two can differ because the source and recipient have different incubation periods, so observed onset timing is not automatically interchangeable with infection timing.^[1]

A recipient can develop symptoms before the source does even when recipient infection occurs later. That gives a negative serial interval without a negative generation interval. Subtracting generation from serial timing reflects the difference between the two incubation durations.

Generation Serial Interval Pairs returns both interval lists and mean serial interval minus mean generation interval. It uses supplied transmission pairs without discovering links or estimating infection dates.

When to compare infection and symptom timing in pairs

Use the tool when infection and onset coordinates are available for the same source–recipient records. It helps check how an onset-based summary differs from an infection-based summary.

Retain negative serial intervals rather than discarding them.
Calculate the signed difference between mean timing measures.
Check infection/onset ordering within each pair.

How to enter paired times and compare the intervals

Enter nonempty aligned Source infection days, Recipient infection days, Source onset days, and Recipient onset days lists.
Use one day axis and ensure recipient infection is no earlier than source infection and each onset is no earlier than its corresponding infection.
Run the calculation and read both interval arrays in pair order.
Read Mean interval difference days as mean serial minus mean generation; a negative result means the serial mean is shorter.

generation_i = recipientInfection_i − sourceInfection_i; serial_i = recipientOnset_i − sourceOnset_i; meanDifference = mean(serial) − mean(generation)

The implementation checks the within-pair ordering and uses ordinary arithmetic means. It does not require records to be chronologically sorted across the lists.

json

{
  "input": {
    "sourceInfectionDays": [
      0,
      2
    ],
    "recipientInfectionDays": [
      4,
      8
    ],
    "sourceOnsetDays": [
      2,
      5
    ],
    "recipientOnsetDays": [
      7,
      9
    ]
  },
  "output": {
    "generationIntervalsDays": [
      4,
      6
    ],
    "serialIntervalsDays": [
      5,
      4
    ],
    "meanIntervalDifferenceDays": -0.5
  }
}

Equal infection times and onset at infection time are allowed. Signed serial intervals and negative day coordinates are accepted when the within-pair rules hold. Empty/misaligned lists, invalid ordering, nonfinite values, or incompatible types produce errors.

Limitations and interpretation

Infection times are supplied as point values; uncertainty or interval-censoring is not modeled.
The tool does not establish transmission direction, identify pairs, account for missing/asymptomatic infections, or fit a generation distribution.
An average difference can hide substantial pair-to-pair variation; no variance or confidence interval is returned.
Generation intervals cannot be negative in this implementation, but serial intervals can be.

Alternative or Complementary methods

Use an onset-only summary when infection times are unavailable. A growth-to-reproduction conversion needs an assumed generation distribution, not an unqualified substitution of a serial mean.

References

How generation intervals shape the relationship between growth rates and reproductive numbers — Proceedings of the Royal Society B; J. Wallinga and M. Lipsitch (2007)

Similar or alternative tools

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