New infections have been declining at an almost adequate pace (10% per week?) in most parts of the US, and probably the rest of the developed world.

The overall reported new cases look more discouraging, for two reasons.

One reason is the increase in testing. I estimate that two months ago, a bit less than 10% of new infections were being confirmed by tests, and I estimate that now it's above 20%, maybe getting close to 25%. That means that if the new infection rate were unchanged, we'd be seeing a roughly 10% per week increase in reported cases.

Nearly all parts of the country have done a good deal better than that.

I estimate the change in new infections since the early April peak by multiplying the early April confirmed daily cases by 10 or 12, and the June ones by 4 or 5, and I get a current rate that's about 1/4 to 1/3 of the peak.

The bad news is that there are some heavily populated areas for which the trend doesn't look very good over the past few weeks. When the rate of new infections remains constant in some areas, but declines at exponential rates in others, the exponential declines stop affecting the total numbers before too long. E.g. much of California has suppressed the pandemic, but a few cities, such as Los Angeles and Oakland, are enough to keep the state's total count of new infections steady.

I'll base this analysis mostly on Alameda county, where I live. It looks like new infections are coming heavily from low-income workers whose jobs require them to meet many people. They presumably get infected on the job, and also spread it within crowded homes.

I presume a nontrivial number of new cases are being reported from nursing homes. That might just be because authorities have finally gotten around to massive testing of nursing homes. I presume that if the spread in nursing homes has not already been reduced, then the new reports will trigger some action to fix the problems there. But there are no videos of, say, Gov. Cuomo directly infecting nursing home residents, and maybe it's hard for the US to do much about deaths that don't generate distinctive videos, so I still have some mild worries here.

I did a cursory check for other problem areas. Elevators? Two nearby cities, Emeryville and Albany, stand out as having a much larger fraction of high-rise apartment buildings. If elevators were an important source of infections, they'd have more cases than surrounding cities. Yet they have hardly any. That's clear enough evidence for me to dismiss that concern with a fair amount of confidence.

How about subways? I haven't investigated very carefully. LA doesn't seem to have lots of people using subways, but it might still have enough to cause the infection levels that we're seeing. The SF bay area subways were nearly empty for much of the spring, and that correlates somewhat with relatively good results in San Francisco, but the Oakland / Hayward area has much worse results, without having heavy subway use. I'm guessing based on that weak evidence that subway use isn't important enough for me to track down strong evidence.

Where do these trends lead us?

Increased testing, plus some rudimentary tracing, are likely just now starting to produce some benefits. Testing apparently became available enough in the past week or so for authorities to do thorough testing of high risk populations. Even half-assed tracing will do more to focus attention on the important sources of new infections. In the land of the blind, the one-eyed man is king. The US has been, in some ways, effectively blind, and is just starting to get some eyesight.

What fraction of these newly detected cases will be adequately isolated? Even if it's just 20%, and the testing has been increased enough in the high-risk populations to detect 70% of infections versus 20% that would have been detected a month ago, then I expect the least successful populations to go from infections increasing at 2%/week, to at least declining at 3%/week.

Presumably it's hard for most of those people to isolate themselves, but local authorities have some ability to increase that isolation rate by offering free special-purpose housing and other support. Will many authorities care enough? That depends a lot on how clear it is that doing so is the only way to keep the local economy functioning. My guess is that it will be mostly pretty clear to them.

Businesses seem to be reopening at a slightly faster pace than tests and tracing are ramping up. That increases the population of people in the stable or just barely increasing infection rate group. But they'll mostly be entering that group with lower infection levels than people who never stayed home from high-risk jobs. So I don't see the reopening as creating much risk that actual infections will rise anywhere near as fast as test and trace will ramp up.

So I'm cautiously optimistic that most businesses can reopen while still allowing us to decrease the rate of new infections. I'll estimate that a 5% per week decrease is a fairly cautious goal. And since test and trace will work better when infections are rarer, we could get a somewhat better than exponential decrease.

That would leave us in September with, at worst, half the daily infections we're getting today - say, no more than 50,000 per day for the US (versus the 100,000 per day that I estimate to be happening now).

Then sometime in the fall(?), a combination of the colder weather, increased complacency and/or apathy, and frustration with masks and modest distancing, will create the second wave. Some areas will contain it with more aggressive methods of isolating people who test positive. A smaller number of areas will reimpose some sort of lockdown.

I would like to end here on this optimistic note. Alas, it only analyzes the effects of reopening the economy. I left out any the effects we should expect from changes in social gatherings.

Churches, protests, and probably large birthday parties are resuming.

The protests won't last long enough to directly create any sustained trend, but they set a conspicuous precedent which will encourage other social gatherings. I don't have much idea whether that effect will be significant.

Churches and large birthday parties seem likely to have some lasting effects on the infection trends. They can be done responsibly, but there are significant social benefits to including singing in enclosed spaces. Churches in particular will feel some temptation to recreate the conditions that are likely to create superspreader events.

Many churches will remain scared enough to avoid riskier practices. Many others will be in areas where infection rates are low enough that they can maybe get away with going back to normal. Yet the riskiest 2% of churches could still generate many new infections, maybe more than can be handled by the test and trace systems that we're likely to get.

Maybe the churches in the riskiest places are the ones who know that they can't rely on experts to make the world safe for them, and they'll decide on their own to take plenty of precautions. Or maybe testing will become sufficient to quickly detect and isolate new breakouts (currently, upticks in new cases are hard to evaluate, because they often just reflect increased testing). I don't see how to get good information on these issues.

I'm left with a disturbingly large degree of uncertainty.

Other thoughts

I'm becoming more optimistic about getting a vaccine by about next summer. One piece of evidence that's been neglected is that other coronaviruses do have commercially available vaccines. Somehow they get neglected because they're for pets and livestock.

Treat Early has some ambitious hopes of testing treatments in pre-symptomatic patients. My initial reaction was that they had little hope of finding infected patients soon enough for that to work. But now I see reports that an app that uses the Oura can detect COVID-19 3 days before symptoms develop. That leads me to think this deserves further attention.

The US government is only making half-hearted attempts to encourage vaccine creation, and even less on understanding the pandemic.

We have a bipartisan consensus that it's more important to transfer money to some affected by the pandemic than to prevent new infections. Most politicians have decided that preventing new infections is approximately priority number 3, and are busy fighting about whether enemy number 1 is racism or lockdowns.

Part of why the stock market is doing well this spring is that there was a concerted effort to convince people that the pandemic is harmful, in order to get them to stay home. And since GDP is good, a harmful pandemic must be associated with a decline in GDP. So it became part of the pandemic-fighting strategy to convince people that a terrible decline in GDP was inevitable. Or maybe people decided to measure the benefits of policies by how much they cost. Or assumed that unemployment causes depressions, when the causality mostly goes in the other direction. At any rate, there was widespread pressure to believe the worst. Now it's becoming hard for the storytellers to ignore the evidence of recovery, and many people have gotten tired of scaring each other into taking the pandemic seriously.

Friday's market rally felt weird. It seemed like a large number of investors suddenly realized that the headlines had been misleading them, and that there isn't much reason to expect a depression (unless what happened in March/April qualifies as a depression). Yet at least half the stocks had already rebounded enough before Friday to reflect a return to near-normal GDP levels.

That still left a fair amount of room for some of the harder-hit stocks to soar (e.g. airline stocks and Hertz that had been depressed by panic selling from Warren Buffett and Carl Icahn). But the rally in the average stock has gone far enough that I switched on Friday from being bullish on the market, to being confused.