COVID-19 March 25, 2020

Some good news? We're still closing in on the 100,000 mark in just a couple of days from now, BUT take a look a the second graph below--the daily rate of change. Yesterday's total showed a drop in the number of infections compared to the day before: 9,905 vs. 10,408. It's hard to say if that is real, which would be good news, or a change in testing, which would not be good news. A closer inspection of the numbers indicates that the drop is largely due to a drop in new cases for NY. The number of daily new cases in NY fell by almost 1,000. Are the social distancing and lockdown policies in NY showing? At the same time, other states are exploding. For example, MA went from 131 to 382. Is that due to increased testing or is it real? And then some states still seem wonky, as I indicated yesterday. Did LA really drop from rising numbers up to 335 the day before down to 216? Seems unlikely. So, the nationwide total could be good news, or it could just be bias in the measurements. We'll have to wait a few more days to see how things go. I do find it interesting that I haven't seen the drop in numbers in the press.

Nerdgasm alert for what follows:

There is no need to be a medical professional or epidemiologist to understand and then predict what is happening. It's simple mathematics that emerges in countless natural systems. If you tell me that the change in some quantity is proportional to the amount of that quantity, I can write down a simple ordinary differential equation (ODE), the solution to which has been known since Newton invented calculus: an exponential function. I could be totally ignorant of the origin of the data I've been plotting, but if you told me that the next number in a sequence of numbers was proportional the current number, I'd know exactly how to model that series without any knowledge whatsoever of the physics behind the numbers. In this case, the number of new infections is proportional to the number of existing infections, at least initially. Thus, it can be described by an exponential function. Similarly, the change in the intensity of light passing through an absorptive medium is proportional to the amount light (a.k.a. Beer's Law) and is described by the same exact ODE with the same exponential solution. It's just math.

Eventually, other things will begin to influence the growth rate besides the existing number of cases. For example, the number of people that have died could start to matter. Those people cannot pass on the infection nor get reinfected (because they're dead). For now, we can ignore them with only a small error, because they are a small fraction of the total population that is alive. But, that may not always be the case, and thus the error of using a pure exponential function will grow with time. And the number of people that have been infected but are fully or at least partially immune to reinfection can also come into play. And there can be subtleties, like having some fraction of the population be more susceptible than others or more likely to pass an infection than others. Or the virus could mutate and change its lethality, viability, or transmissibility. Each of these effects, and others, can be described by other ODEs, all of which then become a coupled system of equations. But, in the end, it's still just math, and there are analytical and numerical ways to solve those coupled equations. My area of expertise requires me to solve even more complex coupled partial differential equations (PDEs), but the techniques for solving ODEs are a simplified subset of the PDEs. It's all just math.

For the analyses I've been doing, I'm only comparing the data to the simple exponential model. The data fits. It works. When the data starts to diverge from an exponential function, as it eventually must, I can try to include the additional complexities that are making it do so, and then project those data forward (I *may* do that, but it's more time-intensive), or I can just note the degree to which the exponential model fails, which is still an informative metric. We aren't there yet. I hope the data will diverge from the exponential model sooner rather than later, and in the correct direction (downward). The sooner the simple exponential model breaks the better.

One of the flies in the ointment (there are many) is that the exponential model can appear to break when it shouldn't. That can happen when the input data is bad. If consistent reporting fails or testing protocols change that will cause a change in trends that is due entirely to how the data is obtained; the data is no longer purely a metric of how infections are changing over time. Unfortunately, this particular fly seems to be increasingly bathing in the ointment.

/Nerdgasm

COVID-19 March 24, 2020

More and more cities, counties, and states are (finally) starting to take action. I find it incredibly frustrating that it took so long. All data, for weeks, has pointed precisely to the current situation with incredible accuracy in the growth rate of infections. We will surely hit 100,000 on the 26th, as predicted weeks ago, for example. Boulder, CO where my workplace is, has now issued Stay at Home Orders. Denver has done the same. My city of residence (Longmont) has not and neither has the State of Colorado as a whole.

Some of the individual numbers coming in from the states are starting to look a little wonky. I suspect it's because of changes in testing protocol more than anything else, but I can't be sure. In Colorado, tests are now only being done for those admitted to the hospital. I know of several cases in my community that were likely COVID-19, but were not tested. Those cases, and surely the majority of others, are not making it into the daily roundup provided by the State Health Departments. One example of inconsistency is in Illinois. The number of new cases over the last number of days was: 134,163,174,296, and 230. There is no reason for yesterday's number to fall. The inconsistent measures taken in Illinois are too recent for them to have an effect. In California, the series of numbers for a longer number of days were 80, 126, 77, 331, 218, 268, and 265. Again, it's hard to see how this is a realistic reflection of the actual situation. The effect on the slope of yesterday's particularly odd tally is notable in the second figure below. Nevertheless, in aggregate across all 50 states, the noise in the individual numbers is swamped by the totals, which continue upward along the exponential curve.

I would expect the increased social distancing measures taken early on in some cities and states to start to show towards the middle to end of next week. Note that the total number of cases will be 1 million by April 3. Perhaps that date can get pushed out slightly, but it seems almost certain that we will cross that threshold. The measures currently in place are unlikely to reverse the trend, only to slow it; the curve is likely to start flattening a bit sometime next week. As I posted the other day, however, it will be hard to detangle what is real flattening and what is due to changes in testing protocol.

COVID-19 March 23, 2020

Nothing new to add today. Just the stark numbers with continued exponential growth. Still on track for 100,000 sometime on the 26th.

I've been taking the dog for a walk every day, and I make sure to maintain a distance of 50 to 100 feet from anyone that might also be walking around. On each day I've noticed young kids on the playground with their parents socializing at the table. That's not how this works. That's not how any of this works. It's why we are going to be stuck in our houses for a lot longer than we should be, and it's why these half-measures and gubernatorial proclamations are insufficient. The reality is that people are selfish and/or stupid. You shouldn't expect them to behave appropriately. Make them.

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.