The rapid spread of Spanish flu in the fall of 1918 was at least partially to blame on public health officials unwilling to impose quarantines during wartime.
That is, they did not want to impede war production by keeping people home. I guess if you are fighting a war that is a hard decision to make. What if you are not fighting a war? Then isn’t a quarantine obvious? There is absolutely no compelling reason to allow free travel and association that guarantees the spread of a pathogen. It is irresponsible to allow that. With proper controls in place, people can work, goods can move, and the virus can be stopped.
2nd and 3rd waves can arise if 1) the virus mutates – only can quarantine, and test again, or 2) people laying low as carriers come out without being tested. A mutation can be deadly, as it was with the Spanish Flu.