One mistake you’re making is the same mistake EVERYONE made until well into this epidemic - underestimating the incredible infectiousness of this disease (which means a rate of transmission that’s through the roof), combined with the fact that it’s infectious all the way through its incubation period. This means that when and if you decide that actually you were wrong and you’d like to slow the rate of infection, whatever you do will do absolutely nothing for five days at least, and it takes maybe 10 days to 2 weeks for the full effect of whatever you did to actually be seen, and you get to decide if it was enough.
So this is how it looks in practise. You’re the mayor of a city of 1 million, you’ve calculated that if the disease just sweeps through it will take out 1% which is 10,000 and this is sad but survivable.
Here’s some other plausible ballpark numbers: You have 200 ICU beds in your city (20 per 100,000 - that’s the norm in the US), 5% of infections need an ICU bed, and half of them are normally full (with other illnesses). Say on March 20th 0.1% of your population has an infection, which means that 1,000 are infected, 50 need ICU beds and of those, 40 will be okay with that care, but 10 will die anyway. Oh, and your growth in the infection rate is 20% (very low, for the ‘not doing anything’ scenario. Here’s how it plays out from here.
March 21st. 200 more people are infected, 10 need an ICU bed. Your ICU occupancy rate is 100 non-covid, 60 covid, 40 free. If this has been growing steadily all feb/march then one of those covid patients resolves (either by dying or getting better), so now you have 41 free beds.
March 22nd. 240 new infections, 12 need a bed, 1 case resolves so you have 30 free beds
March 23rd. 288 new infections, 14 need a bed, 1 resolves and you have 17 free beds. You realise you’re going to run out of beds VERY quickly if this keeps up, so you announce sweeping restrictions. Total lockdown! Nothing happening in the town except essential infrastructure, healthcare, groceries
March 24th. nothing happens to the infection rate, it’s still 20%, because all the new cases are people who actually got infected 5 to 10 days ago before there was a lockdown. 345 new cases, 17 need a bed, 1 resolves, so now you’ve got one ICU bed for all tomorrow’s cases
March 25th. nothing happens to the infection rate, 415 new cases, 21 need a bed, one gets it, the other 20 are all going to die. 16 of them would have lived if the hospital hadn’t been overwhelmed.
March 26th.nothing happens to the infection rate. 497 new cases, 25 need a bed, 2 can get one because today TWICE as many old cases resolved, other 23 die, 18 of them excess-deaths (would have lived with care)
March 27th.nothing happens to the infection rate (we’re still getting the cases that were infected on the 22nd and before, right?). 598 new cases, 30 need ICU, 28 can’t get it, 22 excess deaths
March 28th. Finally the infection rate twitches down slightly, to 18% (this is based off the Italy data). That still translates to 645 new cases, 32 ICU need, 30 can’t get it, 24 excess deaths
March 29th. Infection rate 16%, 676 new cases, 34 ICU need, now we’re up to 4 resolving per day but that still means 30 out of luck and 24 excess deaths, again
March 30th. Infection rate 14%, 683 new cases, 34 ICU need, 4 resolve, 30 no bed, 24 excess deaths.
It’s now been a week since you decided you needed to do something about slowing the spread of the disease and in that time 100 of your citizens died purely from lack of medical care, rather than from the disease.
Here’s how it goes in week 2
March 31: 12% rate 671 cases, 4 resolve, 30 no bed, 24 excess deaths
April 1: 10% rate 626 cases, 8 resolve, 23 no bed, 18 excess deaths. OK that’s still bad but it’s less than yesterday. Maybe you’re winning!
April 2: 8% rate 551 cases, 8 resolve, 15 no bed, 12 excess deaths
April 3: 8% rate 595 cases, 8 resolve, 22 no bed, 17 excess deaths
April 4: 8% rate 643 cases, 12 resolve, 20 no bed, 16 excess deaths
April 5: 8% rate 695 cases, 12 resolve, 23 no bed, 18 excess deaths
April 6: 8% rate 750 cases, 12 resolve, 25 no bed, 20 excess deaths.
At this point you realise that 8% is as low as your rate of increase is likely to go, because people still have a certain degree of contact/transmission risk through healthcare workers, grocery stores and other essential services. Your total number of infections in the city is now about 10,000 - that’s 1% of the population, nowhere near herd-immunity levels or even bringing-down-the-transmission-rate levels. You’ve got about another month till it starts to reach vaguely-plausible lessened-transmission levels, during which time you keep having about 1% of new cases die because sadly they’re just gonna, and a growing number, getting up to four times that dying because they couldn’t get a hospital bed. By the end of the outbreak you actually have close to 50,000 dead in the city, the vast majority of which died through lack of medical care. Oh, and I never modelled-in ‘20% of your ICU staff had to go into isolation because they caught the disease off their patients, and now you only have 160 beds’
You don’t get re-elected