COVID-19 March 22, 2020

The march toward 100,000 cases continues with excellent adherence to the exponential model. 23,640 was the total at the close of March 21, as reported by the individual state health departments. Both the short- and long-term trends predict that we will reach the shameful achievement of 100,000 about four days from now on the 26th. We only passed 10,000 a few days ago.

California and New York are now restricting testing to health workers and those that are hospitalized. This is likely to impact the total statistics, especially since New York currently has over 40% of cases. If the change in testing protocol results in a decrease of reports, it may be hard to detangle any actual decrease (i.e., flattening of the curve) from biased testing and reporting.

At some point, the curves will flatten out. They have to. Exponential growth cannot continue forever. If you take the exponential model I've been using and extrapolate those predictions forward in time, we will surpass 1 million cases in early April, 10 million about 8 days after that, 100 million yet another 8 days later, and 1 billion by early May. That exceeds the entire population of the United States. The exponential model will break down. When it does, there are slightly more complex mathematical models to represent the behavior of the data. These models are well known and understood and generally produce an S-shaped (sigmoid) curve. Once we start to deviate from the exponential curve, I may switch to those more complex models. The question is, when will that happen?

COVID-19 March 21, 2020

I'm a little late posting today's update. I took advantage of the self-imposed house arrest to sleep in.

New reported cases continue to closely follow the exponential model (first figure below). With testing continuing to ramp up, new cases have actually slightly exceeded the model predictions and have caused the curve to steepen, not flatten (second figure below). I do believe this is a bias due to increased testing and not an actual change in the true rate of transmission. Yesterday's numbers bring the short-term trend ever closer to the long-term trend, as discussed in previous updates. The doubling time is approximately 2.4 days now. Just the other day, I noted that we had smashed through the 10,000 mark. It took something like 22 days to reach that point, depending on exactly when you start counting. Some time today, we will almost certainly break 20,000. It took weeks to reach 10,000 and only two days to then double that number. The power of exponents!

A number of states have started to follow California's lead, filling the leadership vacuum at the federal level. New York is perhaps among the most important, as it accounts for approximatley 40% of all cases right now. Better late than never. Some other state leaders still don't get it. They don't think it's bad enough yet. They don't understand that they are one or two weeks away from being New York (see my post from yesterday). With New York, California, and few other states now on some sort of lockdown, the rate of growth in those places should start to slow, but it will take 10 to 14 days before we start to see the effect in the data (also see my post from yesterday). While the new restrictions should help, they may not be strict enough, as we've seen in Italy. Time will tell, but time is also the enemy.

COVID-19 March 20: Update and Some Soap-boxing

The final score from yesterday, March 19, was just shy of 12,000. Not only did the number of infections bust through the 10,000 mark, as predicted, but it did so decisively. This is not altogether surprising. The short-term trend was underpredicting reality because of inadequate testing. Now that the testing is starting to ramp up, the number of confirmed cases is increasing above the predictions that were based on the artificially low numbers. As seen in the graph below, the short-term trend continues to close in on the longer-term trend. Per yesterday's discussion, I expect the orange line to rise above the long-term blue line once testing really gets going. The simple exponential model still does a reasonable job of informing us of what to expect. The next stop is 100,000 cases, and that will be on or around March 26, one week from now. Of course, the large increase in cases over the last day did nothing to help flatten the curve. In the second graph below, you can see the slope not only getting steeper, but rising above both the short- and long-term trends. I'm now also showing the doubling time and decadaling time (increase by a factor of 10), which stand at 2.5 days and 8.5 days, respectively. As in previous posts, click on the images for hi-res.

Today, I'd like to focus on an important point that seems to be lost in the noise: Decisions being made today should be based on what the numbers will be two or more weeks from now. Today's numbers are only relevant in that they can provide a good estimate of what those future numbers will be. There is almost nothing we can do to change the numbers between now and two weeks from now. The cases that will show up over the next two week period are from people that are already infected or will be in the next day or two. The trajectory has been set. Our fate has been sealed. In two weeks, on April 3, we will be approaching at least 500,000 cases if you follow the short-term trend line, or nearly 1,000,000 based on the long-term trend. Given the increase in testing, the 1 million is likely an underestimate. There is nothing we can do about this. Previous decisions and lack of needed action were the recipe ingredients that baked the cake that will emerge in two weeks.

A huge problem is that the media, the public, and the politicians are far too focused on what happened between yesterday and today. How many new cases are there? How many more died? I have admittedly been part of this problem with my previous posts. The real story is that in two weeks we will have something like 1 million infected people. And, that's just the ones we will know about. The actual number is probably many factors higher, because not everyone is tested and some show little to no symptoms. Policy decisions are, unfortunately, being made based on current numbers. That's bad policy. "The numbers aren't bad enough to warrant a complete shutdown of the city or the state", say the mayor or governor. Wrong. Stop thinking about today's numbers, and base your decisions on what should be done if the numbers two weeks from now were staring you in the face, because they will be. And in two weeks, after having failed to grasp the idea of what time does to an exponential function, the same politicians will make the same mistake, failing to recognize that two weeks later yet again, the numbers will be another 100 times larger.

Governor Newsom of California is the first politician to quarantine an entire state. Not just any state, but the State of California. Perhaps he understands that his actions have a two-week delay attached to them. Unfortunately, the state-wide shelter in place probably should have happened two weeks prior. If it had, then the effects of that order would start to take effect today. Instead, we wait, helpless, for two weeks as people get sick and many die. Other leaders in every state need to follow Governor Newsom's lead. We can't wait for the federal government to do it; the person in charge is incapable of grasping the situation.

So, stop focusing on the numbers from yesterday, today, or tomorrow. Think about where we will be in two weeks, because we WILL be there and predictably so. Take actions today based on the future, not on the past and present. What should be done today knowing that in two weeks there will roughly 1 million known cases? What should be done knowing that there is nothing we can do to change the number two weeks from now? What should be done today knowing that hospitals will be well beyond capacity, that there will be insufficient ventilators, that the doctors and nurses we depend on to treat the sick will not have the personal protective equipment they need to stay healthy themselves, and that the people still working the basic services and infrastructure that we need to remain functioning begin to fail? Act today as if it is two weeks from now.

EDIT: I realize I was a little sloppy with my words and in the graph below. Actions taken today can have an immediate effect. But, we will not see that effect in the data for about two weeks. I shall strive to be more precise.

COVID-19 March 19, 2020

A couple of important changes with this update. First, going forward, I will provide an analysis using only the prior day's data. I've had to make this change, because the CDC releases info at noon (EDT) and those data are woefully incomplete and behind compared to the reporting from the individual state health departments. As soon as the day's numbers from the CDC hit the street, they are already obsolete. For example, yesterday's numbers ended up at 8,058 cases, whereas the CDC report from yesterday showed only 7,038.

Second, I am now using wikipedia as a data source, which in turn posts data directly from the state health departments. See here and here. These data are continually updated in near real-time, and are verifiable by going straight to the state health department websites that are given as references for the data.

So, today's update is really a reanalysis of yesterday, but using more accurate and complete data. There's no point in looking at what the CDC will say later today, because the data are still pouring in, and will be continuing to do so until late until the evening. I'll look at those final numbers and report on them tomorrow.

Below is the analysis based on data valid for yesterday (click on the image for hi-res).

As I indicated above, the actual number of cases (8,058) was far above what the CDC had reported at noon (7,038). Including this more accurate data drives the short-term trend line (orange) closer to the long-term trend (blue). I can't be certain, but I strongly suspect that effort to increase testing is starting to show. Still, the number of suspected cases far outweighs the current testing capabilities. As capabilities increase, I expect the short-term trend to approach and then actually surpass the long-term trend. It seems very likely that the slight dip over the last few days was due to systematic bias in testing, and not a true deceleration of the exponential growth.

The short-term trend line is predicting 10,129 cases by the end of the day. That is likely to be low compared to reality and indicates that the short-term trend is indeed suffering from systematic data bias. Using either the short- or long-term trend, the data predicts that we will hit 100,000 cases around March 26, plus or minus a day. This is 10x the current number. If things continue, we will hit 1,000,000 a week later. The 100,000 number is nearly a sure bet. There's nothing we can do about it because the people that will be diagnosed are already infected. If significant actions are taken, there's a chance that we can have an impact on the 1,000,000 two weeks from now. It will be interesting to see if the patchwork of half-assed local and state policies will show any effect; it's going to take more than a week to assess that.

Flattening the curve is a popular meme right now. Below is an analysis of the progress, or lack thereof, in doing so (click on image for hi-res). The graph shows the daily change in new cases. For algebra buffs, each data point shows the slope of the curve in the graph above for each day. For calculus buffs, it's the derivative of the curve above. If the number of cases was to remain the same as the day before, the line connecting two data points in the above graph would be horizontal. Horizontal lines have a slope of zero. Clearly, that's not the case. The line is not horizontal. It has a positive (and large) slope. Right now, the number of cases each day is increasing exponentially, and the slope of the line is getting larger and larger, which is why the line in the graph below is going up. In other words, the curve is not flattening at all. A flattening of the curve would mean that the data in the graph below would start to fall and head toward zero. A value of zero, however, indicates only that the number of cases isn't increasing or decreasing each day. Ultimately, we want the number of new cases each day to be lower than the day before. That would imply a negative value (below zero) for rate of change. We've got a loooonnnnggggg way to go before that happens.

The fate of all these curves depends exclusively on the collective actions of individuals. We must all do our part. Do not go out in public unless it is absolutely necessary. The CDC recommends no groups larger than 10. This is inadequate. Groups no larger than 1 should be avoided. In other words, no groups!

I continue to receive information from my doctor and nurse friends working at local hospitals. They are already running out of beds, supplies, personal protection equipment, and everything else that is necessary to treat the infected. We're only at 10,000. Next week it will be 10x worse, and the week after will be close to 100x worse. The system will likely have exceeded its breaking capacity. Nobody knows what will happen then. There is no plan. In Italy, patients were left to die. It's hard to imagine a different outcome here. Each of our individual actions can make a difference. DO IT.

EDIT:  CDC Website now says the following:
"In the event of a discrepancy between CDC cases and cases reported by state and local public health officials, data reported by states should be considered the most up to date."  The data above are from the state and local public health officials, as indicated.

COVID-19 March 18, 2020

CDC just put out their numbers based on reports from yesterday: 7038.

Today's graph hasn't changed much from yesterday. Note that yesterday's numbers have been adjusted slightly (upward) to account for reports that trickled in late. Today's 7038 will likely be adjusted slightly upward tomorrow.

Based on the orange trend line, we will come in just a little bit under 10,000 tomorrow. For reference, we crossed 1000 on the 11th. So, a 10-fold increase in one week. If the trend continues, we'll be at 100,000 at this time next week. The actual number of infections is probably 10 to 100 times larger.

Medical services are really starting to feel the pressure. I get this info directly from personal contacts I have working at the hospitals on the front lines. If that's what happens at 10,000, imagine next week at 100,000. PLEASE BE RESPONSIBLE and KEEP YOUR DISTANCE. Mortality rate from this is anywhere from 1-5% on average, and much higher for older and higher-risk persons. I'll let you do the math. (What is 5% of 10,000? What is 5% of 100,000? What is 5% of 1,000,000?)

All data except for today is coming from: https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_the_United_States Today's data is from the CDC: cdc.gov/coronavirus/2019-ncov/cases-updates/cases-in-us.html

COVID-19 March 17, 2020

Today's numbers are in. I've updated the analysis a bit. I'm now showing all the data (blue) and the data for the last 10 days (orange). The trend line from the orange data will be more responsive to shorter-term changes. The good news is that the orange line is below the blue, although that could be a statistical aberration or the result of systematic issues with testing and reporting (likely). The bad news is that either line is bad news.

The Cognitive Dissonance of Sam Harris

In “The Moral Landscape”, Sam Harris argues that morality can be determined by considering the impact of actions on social well being.  The impact is quantifiable through the relative comparison of possible social states arising from different actions.  A moral action is one that produces the greatest relative maximum in the topology of possible states of societal well being.  Let us take this definition of morality as an axiom.  For the purposes of this piece, it matters only that Sam Harris believes it to be true not that it is true. 

Now also consider Sam Harris’ position on guns.  He argues vociferously for the right to own guns.  Lots of them.  Of many kinds.  For example, in his “The Riddle of the Gun” he writes:

“Wouldn’t any decent person wish for a world without guns? In my view, only someone who doesn’t understand violence could wish for such a world. A world without guns is one in which the most aggressive men can do more or less anything they want. It is a world in which a man with a knife can rape and murder a woman in the presence of a dozen witnesses, and none will find the courage to intervene.”

This is, of course, a strawman argument.  Few are calling for a world without guns, although it is reasonable to ask whether such a world would be in a state of greater well being than a world where guns are ubiquitous.  Does it really follow that in a world without guns that a man with a knife can rape and murder?  Are law abiding citizens really helpless in a world without guns?  Do we see women being raped and murdered across Western Europe where guns are generally far less common than in the U.S.?  Is crime rampant in the UK where not even the police carry firearms (except for Ireland)?  And, couldn't non-lethal methods be used?  How about tasers or pepper spray?  Are guns the only defense we have against violence?  It's a strawman and a false dichotomy.

The reality is, reasonable people are calling for greatly limiting access to firearms or removing certain types of firearms from society.  Is the resulting scenario a state where well being would be increased?  Suppose only law enforcement carried firearms so as to protect law abiding citizenry from violence.  Would this result in a state of higher well being than we have now?  Conversely, would well being be increased by increasing the number of guns and allowing nearly everyone to carry multiple firearms at all times? 

Measuring well being is subjective, so reasonable people might disagree over whether one possible outcome is better than another.  However, it seems that in the spectrum of possible states of well being, a society in which there were no guns, or at the very least, a society where only law enforcement carried firearms would be better off than a society where guns flow like water.  And a society with non-lethal weaponry might be yet an even higher state of well being.

Sam Harris’ moral landscape position seems incompatible with his stance on gun control.  He has provided all sorts of arguments to support his position on guns, but interestingly, he has not yet, as far as I know, argued his position in terms of the moral landscape.  If morality can indeed be quantified by testing actions against their effect on well being, then Harris’ best argument for guns would be to show that a society armed to the teeth is better off than a society without firearms.  Good luck with that one, Sam.  I suspect that in the end, you'll have to choose either guns, or the philosophy of the moral landscape, or reject both.  But you can't have both guns and the philosophy of the moral landscape.