Originally Posted by
slats11
Correct up to a point ... It is these very experts using the word exponential.
We are in furious agreement. I also said it was exponential. What I objected to was that you calculated using
two data points and claimed that this made the increase exponential. This is mathematically, scientifically and logically wrong. If you don't know why, don't make senseless calculations to draw conclusions that you don't understand. You're entitled to your opinions but not to the facts. Give up gracefully.
I had read the Lancet paper previously, a link to a non-pdf web version is
here. You probably shouldn't quote selected sections of it when a more complete exert says differently. Example, you quoted this:
If the transmissibility of 2019-nCoV were similar everywhere domestically and over time, we inferred that epidemics are already growing exponentially in multiple major cities of China...
Whereas the paper goes on to say this:
Therefore, in the absence of (my emphasis) substantial public health interventions ... local establishment of epidemics might become inevitable. On the present trajectory, 2019-nCoV could be about to become a global epidemic in the absence of mitigation (my emphasis). Nevertheless, it might still be possible to secure containment of the spread of infection such that ... transmission does not lead to a large epidemic in locations outside Wuhan.
Which is also what I said: that a contagious disease spreads exponentially
in the absence of any quarantine or immunisation methods. I even emphasised this.
I can't be bothered going further. Instead a few points about the Lancet paper (which is quite short and clear).
- They showed that there was a "negligible effect on epidemic dynamics" to restricting travel, with very little difference in spread comparing no travel restrictions to 50% travel restrictions (their Figure 4 and associated text); interesting. I wonder if this applies to the international travel bans as well.
- There are four caveats to the assumptions made in the paper that would affect outcomes; one of these was if there is any seasonality in the transmission of the virus, similar to influenza.
I assume that If true this might have an effect on Australia in a few months.
- The assumptions on "cases" are different from the number of confirmed cases published by WHO, John Hopkins etc and used in my post and graph. This doesn't mean the Lancet paper is right and WHO is wrong, or vice versa. They are counting different things. The paper has an expandable panel showing the different definitions of "cases" used by CDC and the Lancet paper.
- The paper covers only cases from Dec 31 up until Jan 28, including the Wuhan travel ban that was instituted on Jan 23, so only five days of the Wuhan travel ban.
Your claim that the Lancet paper estimates 75,000 cases in Wuhan bears closer scrutiny. What they actually say is this:
In our baseline scenario, we estimated that R0 was 2·68 (95% CrI 2·47–2·86) with an epidemic doubling time of 6·4 days (95% CrI 5·8–7·1; figure 2). We estimated that 75 815 individuals (95% CrI 37 304–130 330) individuals had been infected in Greater Wuhan as of Jan 25, 2020.
For a start, the Lancet paper has a different definition of "cases" than the CDC (see above). Secondly, this is their
"baseline scenario" it's not a prediction and it's not actual data. It's what they consider a reasonable baseline to use when comparing the effects of differing transmission rates and the effects of restrictions on travel. It may be close to the truth, or it may not. The
confidence credible interval is very wide (approx -50% to +100%) which shows large changes in the number of cases follows relatively small changes in input.
Thirdly, this isn't necessarily bad news. If the epidemic doubling time is 6.4 days this is a daily increase of 11-12%, less than the daily estimates of 50% (during the same time period as the Lancet study) using CDC case numbers. Furthermore if c. 75,000 have been infected and the death rate is ~300 as at present, this is much better than current estimates of mortality.
This is typical of early stages of disease analysis: trying to estimate the numbers infected. Deaths are relatively easy to count but total infections, including asymptomatic cases, are much harder (impossible?) to count but must be estimated. A larger number of these hidden cases sounds more scary (infection rate is higher) but the consequences are less (mortality rate is lower). And so it goes...