PU650 Unit 2 Transmission Analysis Example

Eighteen Linked Pairs and a Twenty-Four-Day Gap: A Unit 2 Transmission Analysis Estimating the Serial Interval and Reproduction Number of Hepatitis A Among People Living Unsheltered in a Composite City

[Student Name]

Purdue University Global

PU650: Infectious Disease Epidemiology

Unit 2 Transmission Analysis

[Instructor Name]

[Date]

Pellham, its cases and its tracing records are composite; the virus's biology, the estimation methods and the research cited are real.

The Question and the Data

The prompt asks how the virus moved from one person to the next. Pellham's health department has three sources. The first is a line list of 68 cases with onset in the ten weeks from early February, all among people experiencing homelessness or their close contacts. The second is contact tracing interviews that linked eighteen pairs, each an earlier case and a later case with a plausible exposure between them. The third is the weekly case count. The analysis uses the pairs for timing, the weekly counts for growth, and the tracing notes for route. Every figure below is labeled as an effective reproduction number rather than R0, because some residents had been vaccinated or infected earlier and the population was not fully susceptible.

The Eighteen Pairs

1. February 2 to February 18, 16 days; shared tent at the Riverside encampment.

2. February 3 to February 22, 19 days; shared drug equipment.

3. February 5 to February 25, 20 days; same shelter bunk room.

4. February 6 to February 27, 21 days; partners sharing a tent.

5. February 8 to March 2, 22 days; shared cooking pot at a camp.

6. February 10 to March 4, 22 days; shared tent.

7. February 11 to March 6, 23 days; shelter, adjacent beds.

8. February 13 to March 9, 24 days; shared drug equipment.

9. February 14 to March 10, 24 days; shared tent.

10. February 16 to March 13, 25 days; same encampment, shared water jug.

11. February 18 to March 15, 25 days; shared drug equipment.

12. February 19 to March 17, 26 days; partners sharing a car.

13. February 21 to March 20, 27 days; same shelter bunk room.

14. February 23 to March 22, 27 days; shared tent.

15. February 25 to March 25, 28 days; shared drug equipment.

16. February 27 to March 28, 29 days; same encampment, shared portable toilet.

17. March 1 to March 31, 30 days; shared tent.

18. March 3 to April 5, 33 days; same day center, shared meals.

Each line gives the infector's onset date, the infectee's onset date, the interval and the link from tracing. Pairs were accepted only when the infectee reported no other known case contact in the fifty days before onset, the longest incubation period for the virus.

Serial Interval

The script reads the eighteen intervals and reports a mean of 24.5 days, a standard deviation of 4.2 days and a range of 16 to 33. A serial interval is the time between symptom onset in one case and onset in the person that case infected, and it is the bridge between how fast an epidemic grows and how many people each case infects. Two cautions apply. Pairs identified through tracing favor close, repeated contact and may miss brief exposures. And early in an outbreak, short intervals are overrepresented among the pairs observed so far, a bias that would pull this mean slightly downward. The serial interval is shorter than the incubation period, and that single comparison explains why isolating people once they turned yellow did not stop the outbreak.

First Estimate: From the Growth of the Epidemic

Weekly onsets over the ten weeks were 2, 3, 3, 4, 5, 6, 8, 10, 12 and 15. The script fits a straight line to the natural logarithm of those counts and returns a growth rate of 0.22 per week. Growth alone says nothing about how many people each case infects; a fast-growing epidemic could come from few secondary cases with a short interval or many with a long one. The serial interval resolves this. Treating the interval as a gamma distribution with the observed mean and standard deviation, the reproduction number equals one plus the growth rate divided by the distribution's rate parameter, raised to the power of its shape parameter (Wallinga & Lipsitch, 2007). With a mean of 3.5 weeks and a standard deviation of 0.6 weeks, that gives an effective reproduction number of 2.14. The script prints the two simpler approximations alongside it, 1.77 if the interval were exponential and 2.16 if every interval were exactly the mean, to show how much the answer depends on the interval's shape.

Second Estimate: From Counted Offspring

Tracing identified the cases each of the nine earliest index cases went on to infect: 2, 3, 1, 2, 4, 1, 2, 2 and 3, a total of 20. The mean is 2.2 secondary cases per index case. This estimate is direct but fragile: it depends on tracing finding every infectee, which among people who move between camps and shelters it almost certainly did not, so 2.2 is better read as a floor than a midpoint. The two estimates were made from different data, growth from the weekly counts and offspring from tracing, and they agree within a tenth. That agreement is the main evidence that either is sound. An analysis offering only one would have no way to check itself.

Route

Hepatitis A spreads by the fecal-oral route, and the tracing notes describe how in this population. Twelve of the eighteen links involve shared living space without reliable toilets or sinks: tents, a bunk room, a portable toilet at an encampment where the city had removed the hand-washing station in December. Five involve shared drug equipment, consistent with outbreaks elsewhere in which hepatitis A moved through drug-using and unhoused social networks in four states (Foster et al., 2018). One involves shared meals at a day center. No food-handling or commercial product link was found, which fits a person-to-person outbreak rather than a common source.

Why the Interval Is Shorter Than the Incubation

The mean incubation period of hepatitis A is about four weeks, and fecal shedding of virus peaks in the two weeks or so before jaundice appears (Lemon et al., 2018). A serial interval of 24.5 days, a few days shorter than the incubation period, is what that biology predicts: people pass the virus on before they feel ill, so their contacts' onsets come earlier than a full incubation after the infector's own onset. The control implication is direct. Isolation after diagnosis acts too late to break most chains. Vaccinating contacts and the wider population at risk, and restoring sanitation where people live, reaches the transmission that has already happened by the time the first case is yellow.

Limits

The pairs are few and selected by tracing. Onset dates rely on recall in a population with limited access to care. The growth rate assumes a constant reporting fraction across the ten weeks, and a late surge in testing would inflate it. Both reproduction numbers describe Pellham in February and March and will fall as vaccination reaches the encampments.

References

Foster, M., Ramachandran, S., Myatt, K., Donovan, D., Bohm, S., Fiedler, J., Barbeau, B., Collins, J., Thoroughman, D., McDonald, E., Ballard, J., Eason, J., & Jorgensen, C. (2018). Hepatitis A virus outbreaks associated with drug use and homelessness: California, Kentucky, Michigan, and Utah, 2017. Morbidity and Mortality Weekly Report, 67(43), 1208-1210. https://doi.org/10.15585/mmwr.mm6743a3

Lemon, S. M., Ott, J. J., Van Damme, P., & Shouval, D. (2018). Type A viral hepatitis: A summary and update on the molecular virology, epidemiology, pathogenesis and prevention. Journal of Hepatology, 68(1), 167-184. https://doi.org/10.1016/j.jhep.2017.08.034

Wallinga, J., & Lipsitch, M. (2007). How generation intervals shape the relationship between growth rates and reproductive numbers. Proceedings of the Royal Society B: Biological Sciences, 274(1609), 599-604. https://doi.org/10.1098/rspb.2006.3754