Just to be clear about terms, when we talk about pandemics, we have what's called the R value. This is a coefficient that expresses how many new cases will be created on average from an existing case. This number is important, because the trend is exponential. If your pandemic has 1000 cases, then with an R value of 2 it doubles each cycle. So you have 1000, then 2000 new cases develop over the infection's lifecycle, then 4000, then 8000, and so on.

The critical value is R = 1. This means that for each existing case will, on average, create 1 new case over that lifecycle. So you have your 1000 cases, and then over the course of the infection's lifecycle you get 1000 new cases, but they only appear as the old ones resolve themselves, so you end up with a steady stream of cases that never really increases, but never decreases until a sizeable enough percentage of the population is innoculated that your R value drops below 1.

It's where you get the R value below 1 that you see the trend towards zero that you're talking about. If the R value is, say, 0.5, then your 1000 cases creates 500 new cases, then those create 250 new cases, and so on. For reference, COVID-19 has a base R value of between 2 and 3. A typical flu is more like 1.3-1.5, so you understand that COVID-19 is far more infectious.

When you take steps to reduce the spread, you reduce that R number. And while a reduction in that number does help, you're still going to see increasing numbers of new cases, unless you're actually able to get that R value below 1.0.

The problems is that moderate compliance isn't enough to get that R value from 2-3 all the way down to a fraction. If masks are fairly effective at fighting COVID-19, and take an R value of say, 2.5, all the way down to 1.5, does that mean that masks are effective? Yes, it does. But at the same time, you're still above R = 1, so you're still going to see growth in cases.

It's pretty clear that we can get the R value below 1.0. Italy is a great example. They got hit super hard early in the pandemic, and they went into strict lockdown. They don't have the same attitudes among the population, or the same rights, so compliance was much higher. And what was the results? They brought their R value below 1, and deaths slowed to a trickle as a result.

You need real compliance, though. Social distancing that is respected by everyone, no parties, avoiding contact, etc. And if enough spoilers ignore the restrictions, it just doesn't work. And that's what we have in America right now. Our government just doesn't have the same level of control as in Europe, and a lot of people aren't taking it seriously, and the result is that we're struggling to get things under control. It's not that these methods don't work, it's that American culture is too individualistic to get the compliance levels you need to bring an infection like this under control.