If you look closely the mathematics is all Gompertz-Functions. Big expansion in small groups, burning locally too fast to maintain a continuous exponential fire. This results in seasonal dynamics just like a corona-virus.

Usually if you look at death by "date of death" you see Gompertz-Functions all around. If you look at death by "reporting date" you often see a very uneven lag forming some exponentials...

Logistic spread, actually.