In terms of policy (mask mandate? schools open? bars open?) we need to be watching the slope of the log graph, not the height of the linear graph. The former tells us how well or poorly we're managing, the latter tells us how much damage is happening because of our previous actions.
By "we" I mean "pretty much all western governments" with a few exceptions.
You've probably seen versions of this graph recently. It's the EU's case count, on a normal "linear" scale.
What do you see?
Clearly, they were doing OK until sometime in October or late September, and then everything got out of control, right?
Wrong.
It's hard to see it on a linear graph, but things got out of control in mid July, and have been steadily getting worse ever since then. Any small change to transmission rates in July, held constant since then, could have averted this climb.
Linear graphs are good at showing the total rates of illness or death, but they're not good at showing changes in rates, especially when numbers are low.
Here's the same data, on a log scale. Log scales convert exponential increases into straight lines. They downplay the overall change in scale - the second peak is actually 4x more than the first peak, but the vertical scale compresses.
Log scales are good for spotting changes in rates. It shows that, for the EU taken as a whole, the epidemic has been surging since at least the middle of July, growing roughly as quickly as the decline from the first peak came down. That probably indicates an Rt of around 1.1 or 1.2, with cases doubling about every 4 weeks.
There appears to have been a slight increase in the slope in early October, which could be some combination of weather, schools opening, or case load starting to overwhelm contact tracing efforts.
The take-home message here is that this isn't a September or October sudden explosion, it's the end result of more than 3 months of the epidemic slowly accelerating.
The same log chart again, with individual countries added. Germany's current peak is only about 1/12th of Belgium's, but you can see that the slopes are broadly similar and Germany is heading for trouble if they don't (or haven't already) implemented changes that matter.
You can see that several countries had a momentary improvement in August, and Spain improved in late September, but overall the trend has been relentlessly upward since about late July.
The media (and possibly policy makers?) are talking about this as a September/October explosion, and they're missing the true story. This is a story of relaxing things a bit too much in July, and not reacting to fix it because the overall death rates were low enough that politicians weren't ready to take the heat.
There are a lot of things that can influence the rate of spread. (Maximum indoor gathering sizes; partial or complete closure of gyms, bars, churches, restaurants, indoor retail; closure of universities or high schools; discouraging indoor social gatherings, etc.)
Each country needs to adopt enough of them to get their line flat, and enough extra to start trending down. But here's the catch...they need to keep the "flat" mix in place for the long term. They can't put five measures in place, then release all five when the case rate drops 80%; they need to keep most of them in place indefinitely.
That seems to be where western policy falls apart. As soon as the case rate is relatively low, there's strong pressure to "reopen" rapidly because COVID looks like it was defeated. The important measure for decision makers should be the log trend - and they should manage their mix of interventions to keep that slope flat or negative.
There is one upside of planning for the log slope - it lets you be more consistent with the restrictions, making it easier to mitigate the economic and other effects a bit. If bars are going to be closed until next summer, rather than bouncing from closed to 50% to 25% to 100% and back, it's easier to set up support programs for the owners and employees. This notion that we just need to tighten for a few weeks then return to business as usual makes it difficult to implement long-term relief.