I do not think that is what is happening.
End of January:
- Virus spreads from Wuhan to many places around the world, by relatively few people
- this would explain first cases in UK, Germany, Italy etc
- since it were few people and we already knew Wuhan/China was a hotspot, in most places these initial infections were contained, or developed very insidiously. Except Italy
Fast forward two weeks and you're getting an explosion in Italy and a new wave of new cases all over the place.
These few cases outside Italy were fed by Otaly itself, China, Korea, etc... But this time they stuck. It was ti many people.
There are many alternative explanations obviously. But to me it seems almost certain that the first few cases in the end of January were an anomaly everywhere except Italy. So to compare both spreads for your country (if in Europe) you have to start a but later in these countries.
Basically I think if this was a race, Italy is ahead because they started earlier, not because they are running faster.