The virus is certainly quite concerning, but those numbers are misleading. Italy almost certainly has far more than 2263 infected cases of covid-19. 2263 is just the number of individuals that sought medical attention, were given the test, and tested positive.

The big unknown is how many of those that are infected do not even seek medical attention (or were not administered the test). For instance, children appear to show either mild or no symptoms when infected.

Additionaly, speaking for myself, if I came down with something, with mild flu like symptoms, I wouldn't really be going to the hospital. I'd just take some over the counter medicine and power through. I would only seek medical attention if symptoms became severe. It stands to reason that this is how most people would be expected to behave. Therefore, people with severe symptoms would be much more likely to get medical attention, and therefore be tested, and to be hospitalized, or require emergency treatments.. making the stats look a lot worse than they are.