https://cmmid.github.io/topics/covid19/severity/diamond_crui...
and the current number of deaths in Italy: 1809 one could come to the estimate of actual number of infections in Italy being around 180K people. That big number is real only if Italians managed to treat that many cases as good as it was possible before the hospitals were overwhelmed. What's probably true, however, is that their hospitals already reached their limits and now the number of deaths per infection raises compared to the ideal case, lowering the number of actual infections.
But even not using that estimated "bigger number" Italy reports 24747 actually confirmed cases.
And assuming that the DNA analysis of this Italian researches is right, Italy's strain must have reached Italy not before January 19th:
https://www.reuters.com/article/us-health-coronavirus-italy-...
Even starting from one person at that date we get, for the number of confirmed cases a factor of close to 1.2 per day, or for the assumed cases (a bigger number) 1.24 per day. That gives doubling time between 3 and 4 days, and never longer than that.
Note that even a difference of using 24K or 180K infected can't give the factor you suggest: 1.15.
That's only observing Italy. I don't know if you are combining Chinese development, where they indeed contained the spread on their territory, with Europe and the rest of the world, where no comparable actions happened (and the actions taken still haven't significantly slowed down the growth), but if you do, that's not proper use of the data available.
If there really was a 10% "true" growth, and higher growth was just testing capacity ramping up, you would see very few straight lines in that plot. Yet that is what you see in all cases except for China, South Korea and Iran.
Also, you can't look at the world-wide growth rate since January like that, since that includes a period where the total number of cases was totally dominated by Chinese cases, but China had slowed already. Actually, the fact that you get 15% by using this approach which substantially underestimates the growth shows that 10% is way too low.
I think it's reasonable to expect that similar containment measures will be put in place in most countries soon, though, so perhaps it's not unreasonable to take them into account when trying to estimate future growth rates.
† https://en.wikipedia.org/w/index.php?title=Template:2019%E2%...
More broadly, we're currently at 167676 confirmed cases worldwide; the first day we have numbers for is January 16th, when there were 45 cases. It's been 59 days since then (31-16+29+15) giving a 15% daily growth rate
but some of that 15% is the discovery of several thousand existing but previously undetected cases over the next several weeks. So the overall growth rate is a little lower than that 15%.(If the Italians were to keep spreading the disease at this rate, by mid-May they'd have more cases than the entire rest of the world; unfortunately for the plausibility of this prediction, their case count would have to be over half a billion people at that point, requiring vast influxes of guest patients from the rest of the world to meet such a quota.)
I did projections at the beginning of February based on a 3.5-day doubling time (22% daily growth) which was what we seemed to be seeing at the time. They said it would infect the majority of the world's population in February. That didn't happen.
† Hey, I'm guilty of this myself; the last time I kissed somebody I'd just met that day was, like, Tuesday. Here in Argentina we can expect rapid contagion.