Issue 030 - Public health - Contact tracing throughput
How large a contact-tracing force would Congo need?
Reuters reported that Congo's Ebola outbreak was nearing 4,000 confirmed cases, while WHO officials estimated that about 80% of new infections were emerging outside known transmission chains.
The problem
Estimate the number of contact tracers needed to identify and monitor the recent contacts of every newly confirmed Ebola patient.
Convert your result into people currently under monitoring, daily calls or field visits, and full-time contact tracers or mobile teams required.
Is the main obstacle likely to be the number of workers required, or the practical difficulty of finding and repeatedly reaching people across a conflict-affected region?
Because Fermi problems target an order of magnitude, I normally use no more than two significant digits and write most calculations in scientific notation; the Fermi reference explains both conventions.
Before checking sources
Matt's first pass
I assumed the current R value, or new patients from every confirmed case, was about 1.5. I also assumed four days from exposure to becoming infectious, another four days from infectiousness to confirmed diagnosis and treatment or isolation, and roughly 12 potentially exposed distinct people per day. That gave me about 50 contacts before diagnosis.
If we are at about 3,900 confirmed cases, then with an R of 1.5 I treated the most recently confirmed group as about 1,300 people.
recent cohort ~= 3,900 / 3
~= 1.3 x 10^3 people
contacts ~= 1.3 x 10^3 patients x 50 contacts/patient
~= 6.5 x 10^4 potential exposuresIf one tracer spends 5 to 10 minutes on each potential contact, I estimated something like 5,500 to 18,000 hours of contact effort for this group. I then assumed we would want to contact all potentially infected people before the end of a four-day incubation period:
daily contact effort ~= 5,500 to 18,000 hours / 4 days
~= 1.4 x 10^3 to 4.5 x 10^3 hours/dayI took a middle number of about 2,800 hours of calls daily. I wrote that this would require about 94 tracers across 8-hour shifts, but that division was wrong. For my own numbers, 2,800 divided by 8 would actually be about 350 tracers.
Calibration Score
Matt's Calibration Score: 35 / 100
Higher is better: earn points for accurate pegs, sound models, correct math, and a result close to the sourced answer. The image shows percent full of it: 100 minus the Calibration Score.
Pegs: 0/30. Recent-case, incubation, contact-count, and monitoring-window pegs were uneven.
Model: 15/30. The model captured contact workload, but initially missed repeat daily monitoring over the full follow-up window.
Math: 0/10. The upper-range hours arithmetic had a meaningful slip.
Result: 20/30. The final tracer count was within an order of magnitude, but the route exposed process misunderstandings.
Grounding facts
The cumulative case total is not the right denominator for the daily workload. Contact tracing scales with new cases per day, contacts per case, and the 21-day monitoring window.
The 80% outside-known-chains figure matters because it says the current tracing system is not just busy. It is missing enough transmission that the lists themselves are incomplete. More workers help, but only if cases are found early enough and communities can actually be reached.
After checking sources
Check and recalibrate
The first correction is conceptual: this is a stock-and-flow problem. The active monitoring burden is not just today's new contacts. It is the pile-up of contacts being followed for the full 21-day Ebola monitoring window.
One way to build the estimate from incidence is:
active contacts ~= new cases/day x contacts/case x monitoring daysUsing Matt's later corrected setup:
new cases/day ~= 30
contacts/case ~= 50
monitoring days ~= 21
active contacts ~= 30 x 50 x 21
~= 3.2 x 10^4 people under monitoringThat is about 32,000 people who need some kind of daily check. AP's WHO-based report of more than 17,000 potential contacts under monitoring gives a lower real-world comparison point, and AP also reported one recent day with 77 new cases. So a reasonable working range is roughly 17,000 to 40,000 active contacts, depending on the daily case rate, contacts per case, and how complete the contact lists are.
If each daily interaction averages 5 to 10 minutes:
daily tracing hours ~= active contacts x minutes/contact / 60
low case ~= 1.7 x 10^4 x 5 / 60
~= 1.4 x 10^3 hours/day
high case ~= 3.2 x 10^4 x 10 / 60
~= 5.3 x 10^3 hours/dayAt 7 to 8 productive tracing hours per worker-day:
tracers ~= 1.4 x 10^3 to 5.3 x 10^3 hours/day / 7 to 8 hours/day
~= 2 x 10^2 to 8 x 10^2 full-time tracersThat puts the main answer around 200 to 800 full-time tracer equivalents, with a central practical estimate near a few hundred. If we use the WHO-reported 17,000 monitored contacts and 5 to 10 minutes per contact-day, the implied load is about 200 to 400 full-time tracers.
Mobile teams can become the more visible bottleneck. If 20% of 17,000 to 32,000 contacts require in-person visits:
field visits/day ~= 0.2 x (1.7 x 10^4 to 3.2 x 10^4)
~= 3.4 x 10^3 to 6.4 x 10^3 visits/day
mobile teams ~= field visits/day / 15 visits/team-day
~= 2 x 10^2 to 4 x 10^2 teamsThe people count is large, but the deeper obstacle is operational: finding contacts, gaining trust, reaching people daily, handling conflict-zone travel, updating lists, coordinating labs and isolation, and not losing people who move between villages, camps, towns, and borders.
Post-check reflection
Matt's reflection
My assumptions led me to a far too high number for the recent cohort, a too-short incubation and monitoring period, and too high a number for plausible contact exposures, so my mental model for how this might take place was sort of all over the place. I also goofed on the upper end of the range for hours spent calling all the assumed contacts, and I neglected to consider repeat monitoring.
When I get closer to 30 new cases daily x 50 contacts each x 21 days of follow-up, that means about 31,500 active contacts. At 5 to 10 minutes per contact, that is about 2,600 to 5,250 hours per day, which would require about 375 to 750 tracers.
I was close, within an order of magnitude, but not quite right. It still counts as a correct Fermi answer, but it also served to reveal my misunderstandings about the process. Ultimately it looks like the WHO was monitoring about 17,000 potential contacts, so if my other assumptions are correct, that correlates to about 200 to 400 full-time tracers.
That is a pretty large personnel commitment and expense just to do this contact tracking, a huge operation even with an outbreak of a few thousand people. This would have to be handled entirely differently for serious illness outbreaks with more than a few thousand confirmed cases. Clearly a major operation.
Recommended memory peg
For Ebola-style contact tracing, remember active contacts ~= new cases/day x contacts/case x 21 days. Daily staffing is then tracers ~= active contacts x minutes/contact / 60 / productive hours per tracer-day.
Reader results
Bars show how submitted estimates sort into the answer choices from the gut-check prompt.