The more accurate curve is a Logistic Curve. You have to factor in that eventually people become immune or die, and there's a total population ceiling. Obviously, the number of confirmed cases cannot exceed this limit!
There are other fudge-factors as well. There is evidence that the very early stages are not exponential, but possibly quadratic or some other curve, but this doesn't matter very much in the grand scope of things.
If you want to be really pedantic, you have to do Monte Carlo simulations using census and geospatial data for each area, factoring in things like school days, work hours, mass transit usage, and tourism.
However, it turns out that after all that effort you end up pretty much with a logistic curve, the first half of which is barely distinguishable from an exponential curve.
All previous pandemics and plagues have followed curves like this.
There is no magic math formula that will dispel this plague. Sorry.
My main point of contention, is someone has to explain the delta between Italy, China, and Japan.
My favored hypothesis on exposure to local pollution does a decent job of explaining. That said, so far every curve people are looking at assumes all nation's curve should be the same. But they aren't. Not even the cruise ships we have locked up have followed Italy or China style patterns.
To provide an entirely unscientific observation about Japan:
I've been there on month-long holidays for the last three years straight, and the thing that struck me as the most alien was their borderline obsessive hygiene and cleanliness.
I'm sure you all know that Japanese people take their shoes off when they enter a house, right? Well, the Chinese recently discovered that coronaviruses can live on pavement for days in cool weather, and people track the viruses into their apartments on the soles of their shoes. The kids and pets roll around on the carpet, and presto... everyone in the household gets The Plague.
Shops in Japan package everything. If you buy a single strawberry mochi for about $1, it'll come in a tiny little plastic container, which they will put in a little paper takeaway bag, which then they will hand to you in a small plastic shopping bag. They sell individual bananas in plastic shrinkwrap. I shit you not.
All this while the cashier wears gloves and a facemask as standard, way before the coronavirus was a thing.
The bus and taxi drivers all wear white gloves. They have doilies on the seats, and I bet they wash them daily, given how pristine and white they looked.
At shinto temples, the first thing you're meant to do before entering is a ritual washing of your hands with fresh springwater. Then, of course, you take your shoes off.
It goes on and on.
Meanwhile, I regularly see people in shopping centres here coughing their lungs up. On to each other, the food, or just generally into the air to spice things up a bit. We're playing Pandemic Legacy on hard mode.
The cultures are entirely different, and Japan basically didn't even have to change anything to prepare for the coronavirus. They just kept doing what they're doing already...
There are other fudge-factors as well. There is evidence that the very early stages are not exponential, but possibly quadratic or some other curve, but this doesn't matter very much in the grand scope of things.
If you want to be really pedantic, you have to do Monte Carlo simulations using census and geospatial data for each area, factoring in things like school days, work hours, mass transit usage, and tourism.
However, it turns out that after all that effort you end up pretty much with a logistic curve, the first half of which is barely distinguishable from an exponential curve.
All previous pandemics and plagues have followed curves like this.
There is no magic math formula that will dispel this plague. Sorry.