If this was flu, say, with a smaller k then you'd see a more normal exponential increase. With this it probably looked more like 1 person, 1 person, 1 person, 1 person, 1 person, 2 people, 30 people. Even absent protective measures most people who get Covid transmit to 1 person or nobody. But some spread it to dozens of others and a small number to hundreds.

I'd guess this is mostly driven by the orders of magnitude difference in peak viral load we see with SARS-CoV-2? But that's really something that needs research.