Read some statistics on the 30-day mortality for covid-19 patients at ICU. It was 34% for patients that first got treated in march, it dropped down to 19% in april and in may it was down to a mere 4%.Yeah, 4% for may was actually wrong, caused by bug in the system, it was too good to be true. The actual number for may was 19% so not an actual improvement over time.
A university study over flu patients at a hospital (sahlgrenska universitetssjukhuset) found that for 435 laboratory verified flu patients during 2016-2017 that 114 of those cases got the flu at hospital. Its patients that were hospitalized for other illnesses and got the flu symptoms 48 hours or more after they were initially hospitalized.
For covid-19 they found that 10300 people working at healthcare had contracted covid-19 in mid may, which is about half of the confirmed cases in sweden. Sweden did have limited testing availability at the time but during a crisis the most important people ends up ill.