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You're either exponentially growing or exponentially shrinking. (some) People are being more careful or wearing masks, which probably has a bigger effect on superspreader events than just "herd immunity". It slows the rise, but that doesn't mean that without intervention you have escaped the pandemic even though it was tamped down quickly.

I agree that CA (especially NorCal) is probably over conservative... but only because there is so much travel that it doesn't matter if they get to zero, when a few travelers form Arizona, Nevada, or LA (ignoring air travel) will bring it all back in a jiffy. What is likely to be the real boom is when kids go back to school... most of them won't get too sick, but most of them have parents or teachers who will. That's your real second wave when everyone is already tired of caring.

Remember, a guy can have unprotected sex with a lot of women before anyone notices they're pregnant. It's probably 3 weeks from infection to ICU and 5 or 6 weeks to death so looking at deaths or even hospitalizations only gives you informations so delayed it's useless when the doubling time can be 3day (and even when it's 10 days). You're up 10x before you know it...

> You're either exponentially growing or exponentially shrinking.

That's what the math says should happen. It's not what the measurements say. If you look on http://91-divoc.com/pages/covid-visualization/ you will see country after country goes linear. The USA for example had 30k new infections most day for a remarkable 2 months.

I have no idea what causes it. It could be measurement error (that's what I first put it down to in the USA). But if it is it damned hard to explain why it has happened over and over again. Russia has been sitting on 9k new cases per day for 2 months now. The UK went through a period of 5k new cases per day for a month.

It's not a universal, or even the most common pattern. But it happens enough to make the statement "the measures of new covoid 19 cases always change exponentially" wrong enough to be effectively useless as a prediction of where things will head.

Any exponential close to 1 looks linear for relatively long periods of time. That doesn't mean that if you "open up" the economy it will stay that way. Unfortunately, the heavily delayed hospitalizations and deaths are the only direct measures, while sampling rates/biases make even statistical analysis of positive tests for infection rates difficult.

However, rising %positive and higher reported rates together or rapidly rising hospitalizations (eg. rising even 5-10% per day) are indications that by the time any new (present day) controls have effect on measured outcome (20-30 day delay) the situation will be 5-10x worse.

> Maybe the R0 curve just flattens more quickly than we thought?

I think that's a confusion of R0 with Rt, Rt is what is influencing what we observe and simply not a constant, and additionally not the same in different settings or states:

https://rt.live/

More importantly, for the Rt == 1 (and being constant) the number of cases would be constantly growing linearly. Only for Rt > 1 the growth is exponential.

As long as the Rt is around 1 it is not surprising that we don't see long lasting exponential growth.

But also note that the values calculated there are more an "illustration" of how the past partial data can be fit to some model than a certainty of the present. The model is helpful to allow us to have a possibility to talk about some concept (Rt and the differences in growth), but is not the current truth, especially for the situation where the data isn't complete and there is a delay in obtaining the updates versus what is actually happening at the moment at every place during the ongoing pandemics. Those who aren't in statistics now can be already infected and die in some weeks, or infect others, and we are never sure how much of those there are at the moment, given the constant changes of the behavior and the movements of the people.

Thank you, I do mean Rt (being the R at time t) at least in the context of the current state of SARS-Cov2 for this discussion.

I think what you’re seeing is exponential growth. Meaning, after crushing the curve, things start all over again with slow growth and then pick up again in 2 months. We are beginning to see the exponential growth explode in Arizona, Texas and Florida now I think.

I'm not sure how it's exponential, if you look at the graph for the current # of cases [0], then you can see it's more or less flat (and the new case %-age has been around 2-3%), between deaths and (most) people recovering, the number of active cases must at least flat and most likely getting smaller?

[0] https://en.wikipedia.org/wiki/COVID-19_pandemic_in_Massachus...

> We are beginning to see the exponential growth explode in Arizona, Texas and Florida now I think.

We will see, I would not bet on it but that is certainly possible.

It’s my understanding that Massachusetts testing has been way down recently which could account for the lower number of positive tests.

Number of daily tests has been broadly flat for the last three weeks and is ~20% lower than the peak testing in mid-May.

It's difficult to match new case numbers against specific tests given aggregated data sources, lag etc., but the rough positive test percentage looks like ~2-4% currently vs >10% mid-May and >20% in April:

https://covidtracking.com/data/state/massachusetts

Exactly. Things with R0 < 1 will fizzle. Herd immunity is 0. Little mathematical exercise. For Massachusetts:

a) Take the number of deaths per day, divide it by the total number of deaths. f'/f.

b) Take a look at this in a log-chart. Use 7 day averages for f' and f to get a cleaner picture.

You will see that f'/f falls down exponentially since pretty much the beginning.

c) determine the exponent by estimating the derivative ln(f'/f)'.

d) Now use that to calculate the function f.

e) Calculate an enddate when it will fizzle.

If people are infectious for some finite number of days, f'/f will always tend to zero, even if f' stays constant.

It falls down exponentially! Just look at it. If you do a bit of math you will see that f will just converge.

I think it really depends on your underlying dynamics, but I just want to point out that f'/f going to zero does really not imply that f will converge.

If for example you are in a still strongly growing (but no longer exponential) regime where you can approximate the currently infected number of persons as proportional to t^2 , and there is some constant IFR, then f'(t) is also proportional to t^2. f(t) will then be growing as t^3, so f/f' will go as t^-1, which will look quite similar to an exponential decay at the timescale of the process.

And I still politely ask you to just look at the data. There is nothing in the data that points to "somehow" and "maybe". It is just a straight linear line in the logscale.

You may see some wobble caused by outbreaks here and there, but the mechanics of COVID-19 are always the same.

Going to zero exponentially does mean it will converge mathematically. And t^-1 won't look like the things that can be observed. There is no such thing as a constant upward trend away from the exponential. If you look carefully and do some regressions you can see some ups and downs. Changes in the behaviour of the people are able to modify the trend, but there is no constant movement away from an exponential.

You can always add an upper exponential bound that will converge below single digits per day before there is any chance that the lines cross.

I'm not doubting that it looks like what you say for the area you looked at. I just wanted to make a more general point that it is not sufficient to look at f'/f and conclude that things will be fine if that is tending towards zero.

I'm not claiming that is what you were saying, I just wanted to call out this point in case other people read this that may come to this conclusion.

FWIW, the solution to f'/f = exp(-t) is f(t)=c*exp(-exp(t)), which actually looks like an epidemiological curve, but like any sigmoid it will be hard to determine the actual saturation point until after it has already passed the inflection point.

Yes, it's important to go down exponentially - which exactly is the thing it is doing - not just in one place...

Good luck that most countries on the planet have already passed the inflection point, so finding the saturation point isn't that difficult anymore.

Interesting to see that just asking people to look into this will generate downvotes. It's just basic mathematics. And it really isn't that hard to verify...

I think the downvotes were not for asking people to look at it, but because the comment can come off as overly dismissive of the severity of the situation.

Maybe, I'm not really a polite person. I think using a working formula for f would greatly help to evaluate the consequences of actions and helps to detect outbreaks early.

In my area they made masks mandatory and cut down the protection of hospitals - now we have an infected nurse. I think politicians currently are using seriously wrong models for their actions.

I had a discussion with one of the "official" epidemiologists. It went like the discussion with you - just at the point where we are now he decided to go into all-caps swearing, said that he will never look into this, called his models perfect and then blocked me.

That's what bertheb says, R0 depends on the other variables, like density, climate etc etc.

> In Massachusetts (where we have been hit pretty hard by C19) we're trending downwards in a significant way and have been for a few weeks now.

Same in California - corona is a health care non-issue here, aside from our governor running for President soon, so it's a political issue. So we'll be the last to leave lockdown, and it's looking like Jan. 2022 now.

By non-issue, I mean hospitalizations and deaths according to the official data have been at the same low rate for months, basically flat. California never had a ventilator or ICU shortage at all. (Last time I checked, we had 58 total deaths in SF/Santa Clara County with millions of pre-lockdown arrivals from China.)

I'm not sure if you're talking about daily deaths, or in total, but California has had 5,286 deaths as of today, not 58. We also had 81 deaths today specifically.

In a perfect world, the point of a lockdown is to arrest the spread of a disease entirely. Unfortunately, we're well past that point in the US. Having failed at that, the goal is not just to keep health care utilization below capacity, but also to buy time to mitigate the disease, by stockpiling PPE and health care supplies, implementing robust contact tracing, and establishing policies for individuals and businesses.

California has been prudently relaxing restrictions for a month now, and is now in Stage 3 of the reopening plan.

They probably meant per day. I think "flat" is a fair characterization of the metric:

https://i.imgur.com/zZ7UGVW.png

Deaths has a few problems. One is that once SARS-CoV-2 finds a nursing home, it's a lot of at-risk people in once place, so it gets hit hard. If deaths is the metric you care about, it's best to put a lot of effort into testing workers at care facilities and putting those facilities strict lockdowns. Once we learned this, we started "gaming" the metric a bit. The other problem is it's a lagging indicator.

Positive tests are problematic because early on, there was a shortage, presumed positive people weren't being tested because it wouldn't change anything, people without symptoms aren't being tested, etc. It's the flakier metric, for sure.

For how many tests are coming back negative, I wish we were doing random testing and random antibody testing. If we're not doing those, we're still being reactive.

> https://i.imgur.com/zZ7UGVW.png

I'm assuming the peaks and valleys correspond to weeks, but why are deaths correlating so strongly with the day of the week?

That's probably an artifact of the reporting process. Most hospitals don't report during the weekends.

Indeed - there have been many cases of where when things have been reported is what gets graphed instead of the actual dates of particular statistics.

The lack of consistent context and framing around the human malware has made most discussions of it pretty useless, but easy to skew in a particular direction for those wishing to make political hay out of a trend (on either side - very few have clean hands in this regard).

I also wouldn't be surprised if there seasonality in medical care, like people receive worse care certain days, for some reason.

58 total deaths for the SF Bay Area in 2020, out of about 4 million people.

The positive rate for 2020 of all tests is 3%, but it really appears that whatever tests they're using are just wrong - California had daily flights from Wuhan.

The one logical conclusion from this thread is that if ships, hospitals and nursing homes have high rates of infection, and California homes don't, turn off your central AC and heating in NY, etc.

The number of deaths for the SF Bay Area is not 58, either. It is:

San Francisco: 47 Alameda: 116 Santa Clara: 152 San Mateo: 99 Contra Costa: 50 Marin: 18 Solano: 23

In other words, about ~500 deaths. If you had 60% of the population infected, you might expect 20x that figure.

Why would it matter that California had daily flights from Wuhan? It changes the math almost by nothing. Whenever an initial seeding occurs, domestic cases rapidly and overwhelmingly takeover in spread.

Wuhan has, as of early June testing, a SARS-CoV-2 seropositive rate of approximately ~3%. There were very few infected people coming on those daily flights in January, and by February domestic spread was many orders of magnitude larger than any seeding event.

California also shutdown earlier than other states, especially in the Bay Area, where essentially all major employers implemented work from policies 7-10 days before the official Shelter-in-Place notice.

California may have had an earlier seeding, but we know for sure it was spreading domestically by mid-January in several cities around the country.

>I'm not sure if you're talking about daily deaths, or in total, but California has had 5,286 deaths as of today, not 58. We also had 81 deaths today specifically.

They are talking about total deaths, but only in SF/Santa Clara. The actual figure is 47 for SF and 151 for Santa Clara [1][2].

[1] https://data.sfgov.org/stories/s/fjki-2fab

[2] https://www.sccgov.org/sites/covid19/Pages/dashboard.aspx#ca...

> In a perfect world, the point of a lockdown is to arrest the spread of a disease entirely.

The problem with this is, that the whole world has to stop for that to happen, and by stop, i mean stop entirely.

Even if you stop the spread in California, and have zero infected people there, the first infected outsider that comes into the state, will spread infections, and you're back at closing down everything.

Basically the second part (keeping healthcare system managable, and hoping for a vaccine soon) is the only think we can do.

Are you ignoring LA county? It's rising rapidly there and starting to spread to the surrounding areas. The wealthy So. Cal. residents who haven't fled yet will move North and then the North will get hit, kind of like what happened to Connecticut via MA and NY.