Quick-and-Dirty Estimate of Number of nCoV2019 Infections in Wuhan

This post concerns the very rapidly developing story of the new corona virus (nCoV2019) outbreak in Wuhan, China.

Let me begin by saying I’m neither an epidemiologist nor a public-health expert. Here are a few of the people I follow on Twitter who have way more expertise than me in these areas:  @HelenBranswell @neil_ferguson @nextstrain @mlipsitch

However, I think about populations and parameter estimation a fair bit in my work on microbial population dynamics.  I wondered about the implications of the fact that there are already 5 cases of travelers from Wuhan into the US who have tested positive for this virus.  That fact made me think there must be quite a large number of infected people (including, thankfully, many for whom the infections are not severe) in Wuhan.

So here’s a quick-and-dirty, rough-and-imprecise, laden-with-assumptions estimate that I obtained for the number of infected people in Wuhan.

a)  China has ~1.4 billion people, and Wuhan has ~11 million, so the latter makes up ~0.8% of the Chinese population.

b)  In recent years, ~3 million Chinese travelers have visited the US per year. Naively extrapolating from the above, that would imply ~24,000 from Wuhan per year, or ~500 per week.

c) In the past week or so, 5 travelers from Wuhan to the US have been found to be infected with nCoV2019. Naively extrapolating again, that suggests an infection rate of 5/500 = 1.0% of the Wuhan population, or ~110,000 infections in that population.

d) Interestingly, this falls right in the middle of another estimate (performed very differently, I presume) from @neil_ferguson (Imperial College) who suggested a possible range of 30,000 to 200,000.

e) There are many large uncertainties associated with my crude estimate. Here are just a few of them:

  • The small number of US cases introduces great uncertainty, in terms of sampling uncertainty alone.
  • Given the on-going spread of the virus, and the fact that these travelers might have visited Wuhan a week ago, this estimate would be outdated and a current estimate would be higher.
  • Travel is not uniform seasonally (and this outbreak corresponds with holiday periods on both ends). I also understand that Wuhan has many universities, and there may well be a disproportionate number of travelers from Wuhan at this time of year. This would imply fewer infections in Wuhan to produce 5 cases here.

I welcome any comments, corrections, and criticisms.

NEW INFO 1:20 pm (Jan 27):   Here’s another interesting (and concerning) bit of data from the CDC. So far, 37 cases have been investigated.  Of these, 5 have been positive, and 32 negative. However, there are 73 more cases with pending test results in just this first week of CDC data. If the % positive holds in these pending cases, that would triple my estimate of proportion & number infected.  That is, the product (5/37) x 73 suggests that an additional 10 or so infected individuals will be identified as having entered the US in this first week. Again, this is a crude estimate with assumptions, and these potential cases are also presumably in isolation, etc.

NEW INFO 2:00 pm (Jan 27):  On Twitter @afferent_input found monthly data on visitors to US from China. Seasonal data suggest number of travelers in this period might be ~2X higher than my crude estimate, which would reduce the inferred infection proportion and numbers relative to my initial estimates. This factor and the other new info posted immediately above might roughly cancel. Again, all of this information is rough and crudely extrapolated. And none of it bears on critical issues of distribution of severity of infections, etc.

NEW INFO 11:00 am (Jan 29):  A bit of good news from CDC. Now 5/73 = 6.8% tests of potential nCoV2019 cases in US have been positive to date. It had been 5/37 = 13.5% at last update. That means no new confirmed positive cases in US. As expected given the spreading infection and expanding concern, the number of pending (unresolved) cases has increased.






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