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My brother in law got chickenpox, yet somehow he didn't infect my two nephews, even though they are living together. According to wikipedia, varicella has an infection rate of 90%:

Varicella is highly communicable, with an infection rate of 90% in close contacts.

https://en.wikipedia.org/wiki/Chickenpox

He got varicella over a week ago and the children are completely healthy, even though they have not had the disease yet nor are they vaccinated against it.

How is this possible? Is the infection rate actually lower, than 90%? Is an outcome like this usual or plausible?

edit: they did end up getting sick after all.

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    Adults with primary VZV infection (chickenpox syndrome) are usually VERY sick, often with interstitial pneumonia, and often require hospitalization. Are you certain he didn't have secondary VZV infection (shingles syndrome)?
    – De Novo
    Commented Feb 18, 2019 at 23:40
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    How infectious you are also depends on your behavior. Your BIL will be much less infectious if he’s using proper hygiene like coughing/sneezing into his elbows, washing hands after using a tissue or scratching itches, keeping distance while talking etc. Statistics can’t account for individual cases.
    – Michael
    Commented Feb 19, 2019 at 7:55
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    If this were in the Puzzles SE, I'd say the answer is in this sentence... 'My brother in law got chickenpox, yet somehow he didn't infect my two nephews,'. It could be your other brother, so he's not a close contact of HIS nephews... I got the wrong end of the stick here.
    – AJFaraday
    Commented Feb 19, 2019 at 9:03
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    How sure are you the nephews haven't caught it? Chickenpox is less severe in the young, and natural variability sometimes means it's almost asymptomatic. My aunt's case of chickenpox when she was quite young manifested as a single bump on her arm, with no other symptoms; the bump probably would have gone unnoticed if other members of the family hadn't come down with chickenpox at the same time. It's entirely possible the nephews caught it first, had asymptomatic cases, and infected the father.
    – ShadowRanger
    Commented Feb 19, 2019 at 15:25
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    @Tim Nevins: yes you missed this sentence in the description: “they have not had the disease yet nor are they vaccinated against it.”
    – Laurent R.
    Commented Feb 19, 2019 at 17:52

3 Answers 3

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To add to @BryanKrause's answer re: rare events happen all the time, the children are not out of the woods yet. The mean incubation time for a primary VZV infection (the clinical syndrome known as chicken pox) is 14 days, but often lasts up to 21 days (see Murray Medical Microbiology, Ch. 53). The father is infectious while shedding virus, usually via the lungs. This correlates with the period of time a patient is febrile. I wouldn't say the father didn't infect his children until he has been afebrile for 21 days.

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If there was close contact, if the 90% rate is accurate, and if occurrence is independent in related individuals, then you would expect 0.10 * 0.10 = 1% of contacts with 2 potentially vulnerable people to result in neither person infected.

1% sounds rare, but rare events happen all the time, and 1% isn't even particularly rare. If you know 100 families, you'd expect this outcome to happen on average in 1 of them.

That's not very unusual and is clearly plausible just from the information you have at hand. As @DeNovo mentioned in a comment, it is also likely that the spread is not independent, because the children share several characteristics: they are related, so they share:

  • any genetic component to vulnerability
  • any characteristics of the father's illness such as the level of virus replicating in the father's lungs
  • perhaps the level of actual contact with the father and how well he may be effectively quarantined from the others

Those factors could make the joint probability across the two children closer towards the 10% rate for a single individual: once you know if the first child is infected or not infected, you can make a better guess about the second child based on all the possible shared characteristics of the children or the infected person.

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    Comments are not for extended discussion; this conversation has been moved to chat.
    – Carey Gregory ♦
    Commented Feb 20, 2019 at 1:24
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Apart from not getting infected due to pure chance (as mentioned already) there is one highly probable explanation (explanation, not overall chance).

People get, but don't show it:

asymptomatic infection

Asymptomatic infection is unusual, but some cases are so mild, they go unrecognised. The primary viraemic phase is followed by a secondary viraemia to the skin and the mucosal surfaces.

Chickenpox (varicella zoster) - Clinical Review, GP-online, 2014

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    Yes, this is an important additional piece of information. The 90% figure is almost certainly based on serology, not the appearance of a rash. Thank you for adding this!
    – De Novo
    Commented Feb 20, 2019 at 13:53

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