One goal is to flatten the curve so that we don't have exponential growth The aim of mitigating measures is reducing the growth rate of the disease. But the me

One goal is to flatten the curve so that we don't have exponential growth The aim of mitigating measures is reducing the growth rate of the disease. But the mechanism of the disease is that you generally have a basic situation where X people infect at time t results R*X people at time t+1. That's fundamentally exponential process (even though you can extra factors, the process doesn't change 'till you get close to having infected everyone). If we can make R small enough, this become exponential decay, a good thing but still an exponential process. But when you do exponential growth. you have a doubling and on the last double, you get more cases than all the cases combines. So the peak is just MUCH higher than the rest of the curve and you can "flatten" a lot and still wind-up overwhelmed in the end if the growth process continues.