The difference between the common flu and Covid-19 is the difference between 1.3^10 and 3^10: 59,000.
That is some important math. The infection rate is so high not only because COVID-19 is highly contagious, but also because there is apparently no pre-existing immunity.
However, it's a very simplified story.
Assuming those base numbers are correct, it's more accurate if less dramatic to say that it's 1.3^X vs. 3.0^X, where X is the number of times the disease has been spread by current carriers to new patients. That simplified model (accurate only for initial spread where the base infection rate stays the same) looks like:
| Generations: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 1.3^X | 1.69 | 2.2 | 2.86 | 3.71 | 4.82 | 6.27 | 8.16 | 10.6 | 13.78 | 17.92 | 23.3 | 30.29 | 39.37 | 51.19 | 66.54 |
| 3.0^X | 9 | 27 | 81 | 243 | 729 | 2,187 | 6,561 | 19,683 | 59,049 | 177,147 | 531,441 | 1,594,323 | 4,782,969 | 14,384,907 | 43,046,721 |
That shows the idea of why it spreads so fast, but it's not a strictly accurate model.
'X' is approximately the same as incubation period+illness period, although in practice disease don't propagate in discrete generations like a simple computer simulation (epidemiologists do more complex math to account for that, of course). Also there is probably a couple days early on where you are incubating but not yet contagious.
Also, in real epidemics the base number shrinks as the epidemic grows. The real number of new cases is not (# of exposures * infection chance), it's (# of exposures * (infection rate - "already sick or immune" proportion). Once 57% of the population already is or has been sick, the remaining spread will look like the beginning of a seasonal flu epidemic. Once more than 67% of the population has already been sick the base new infections (# of exposures * (infection rate - "already sick or immune" proportion) will be less then 1, and the total number of cases will start to shrink.
Of course, governments are also trying to reduce the infection rate by reducing the number of exposures. Where they succeed the virus could be contained before it naturally fades out. At least it will slow the spread dramatically for relatively modest success in reducing the number of exposures (you could work out a similar table
for e.g. 2.5^X to approximate a modestly successful exposure reduction, or whatever base number you believed would be the result of a given policy.)
