Right off the bat, I’ll say that this post won’t answer the question posed in the title—it will merely examine one methodology for addressing the question. And, obviously, I’m not an epidemiologist or any kind of expert. That said, I’ve found a way to look at the pandemic that has given me some measure of relative peace vs. just freaking out.
By the way, for once I’m not going to try to make this a funny post. If anybody finds humor here it’ll be months or years from now when the puny perspective and inevitable inaccuracy of my model and approach will be glaringly, laughably obvious in retrospect.
Who needs a model?
For me, one of the most stressful aspects about this situation is that not only do we not know how it’ll end, but we have no idea when. At least with a final exam coming up or a term paper due, we know when our stress will be over. For better or for worse, that final will be done at 4:00 p.m. on Wednesday, May 27. Whatever kind of shape that essay will be in on Friday, it’ll have been turned in and that’s that. As badly as we’re suffering on a long climb during a bike race, we know there is a summit, and at what mileage or altitude we’ll reach it, even if we haven’t raced the course before. With this pandemic, though, nobody knows where the finish line is. Could this go on for years? It could … the world has seen that before. Not knowing adds to the emotional strain.
Isn’t it enough to follow the news? Well, that hasn’t really helped me. Not only is too much news just depressing, but there’s just not enough consensus to be useful. The media points out what is salient, and discord usually is. Meanwhile, much of what we read is speculation about what could happen (the “news” being that somebody said it), without much effort to say which scenario is the most likely. News is divergent, not convergent.
My solution is to create a mathematical model to forecast the arc of this pandemic. Though this model is extremely crude, it has the ability to improve over time, and at least it’s based on numbers. It gives me some peace, so I figure it might help you, too … but only if we are in basic agreement about what will end the pandemic.
The end of COVID-19: two scenarios
If we could plumb the collective consciousness of the people, across the entire spectrum of humanity, we’d come across all kinds of notions as to how this situation will be resolved. There would be the vague hope that somehow it’d just end, like it would just go away, the way mad cow, SARS, and Ebola seemed to. We’d also find various flavors of denial that this virus actually exists at all, and/or that it’s actually worse than the flu. But if we’re going to try to be reasonable about this, I think we should limit the possible resolutions to two scenarios: 1) enough people are infected that virus can’t find any new hosts (i.e., we reach herd immunity), or 2) a vaccine is developed. Now, if you disagree that the resolution will probably take one of these two forms, that’s totally fine … but you might as well stop reading here. I don’t want to waste your time.
I think it’s possible that a vaccine will come to the rescue. I don’t think anybody is ruling this out, and obviously loads of people are working on that vaccine, and this work simply has to happen because future waves of this coronavirus, or the next one, are probably inevitable. All this being said, I have two problems with hanging my short-term sanity on the prospect of a vaccine.
First, the existence of an effective vaccine doesn’t equate to a swift and efficient means of rolling it out in this country. Vaccinating people isn’t as easy as rolling out a new software version to phones or computers. America is really good at making money, but not very good at making good healthcare available to our entire population. If our performance thus far during this pandemic is any indicator, the time between somebody in this world developing a good vaccine and Americans actually getting it could be very long.
Second, creating a vaccine takes as long as it takes … we can’t just slap a launch date on it. Any time lots of people collaborate on something complicated, delays are inevitable. I have worked in tech for almost 25 years and have seen more deadlines missed than achieved. The only engineering deadline that had any teeth was Y2K, and the entire industry breathed a huge sigh of relief that we fixed our networks in time for that. But Y2K was a lot simpler than a vaccine … it was just cleaning up sloppy software.
The conventional wisdom around the rough timeframe for a vaccine, to the barebones extent I’ve investigated it, is at least a year. WebMD, for example, says it’s 12-18 months out. I suspect herd immunity will come before then, because that’s what my model predicts. If it seems reasonable to you that herd immunity could be achieved before a vaccine, read on.
My pandemic prediction model
I’ve hunted around a bit to see what the generally accepted rate of infection is for achieving herd immunity—that is, the point when the virus can no longer spread due to lack of available hosts. The number I’ve settled on is 70%. (It’s not that important that you agree with this figure because it’s easy enough, with the spreadsheet, to swap it out for something else, which I may do if suddenly all the experts are saying we need 75%, or only 65%.) Multiplying 70% by US population, I come up with 230 million who need to be infected before the virus stops spreading. If we reach that number before 12-18 months, that’ll be the end of COVID-19 in this country (assuming we have some combination of worldwide herd immunity and international travel restrictions).
To figure out to long it’ll take to reach this level, we have to calculate what the current rate of infection is. I’ve been watching the daily stats on Infection 2020, a website my daughter alerted me to. It compiles data from a number of sources: the website cites “CDC, WHO, The New York Times, JHU, Corona Data Scraper, and official state and county health agencies.” Every day, it posts the rate of increase vs. the day before.
Is this website perfect? Of course not. One of the most maddening aspects of this situation is that we can only really guess about how many people have actually been infected with this coronavirus, given the abysmal state of our testing capability so far. I have no doubt that hundreds of thousands of infections, perhaps a majority, have not been documented. But I think it’s still worth using this data, because it will get more accurate over time, and I think you have to start somewhere … otherwise you can’t model anything and your take on the situation will get yanked in too many directions.
When I created my model a little over a week ago, I’d been watching these stats for a couple of months, during which period I’d seen the rate of growth fluctuate between 1 and 4%. It was mostly around 4% at first, and then gradually dropped. Lately it’s been 2% or 1%. The problem is, the growth rate figure is not very precise—it’s only one significant digit—so it flip-flops between 1% and 2% based on the time of day when I check. That’s all the difference in the world.
To get past this imprecision, I created a spreadsheet that models three different growth rates: 2%, 1.5%, and 1%. I started with the actual values as reported by the website on May 16, and copied the formula [previous value * 1.02] down far enough to where the total cases reaches (roughly) 230 million. Here is what the 2% growth forecast looks like (with a ton of rows omitted so the snapshot is manageable):
What the above shows is that if the infection rate proceeds at 2% day-over-day growth, we’ll reach the necessary 70% infection rate by the end of January, next year. Now, of course the infection rate won’t be constant like that … it is bound to go up as we relax the shelter-in-place rules. Or maybe it won’t … many seem to think it’ll flatten out, and for the last couple of months it has. But at least this is a starting point, and it’s easy enough to tweak the model and the situation changes.
Here is the next tab of my spreadsheet, based on a forecast of 1% day-over-day growth in the infection rate:
It has this pandemic lasting until October 5 of 2021 unless a vaccine comes out before then. Is that realistic? Perhaps not, but no matter: I also did a 1.5% model:
The 1.5% model has us reaching herd immunity toward the end of next April.
Now, all three models project a 6% fatality rate, because that number hasn’t changed in months. You may be wondering if I truly believe this pandemic will kill almost 14 million Americans. No, of course I don’t. Keeping in mind that most of the cases we know about are people showing bad enough symptoms to get tested, they’re probably the more vulnerable populations. As more and more people get the virus, we’ll be into the more mainstream cohort: younger and healthier. Meanwhile, as mentioned before, surely countless people have had this virus, or have it now, without being tested. The fatality rate is deaths divided by known cases; as the number of known cases grows, outpacing the deaths, the known fatality rate will fall dramatically.
So which of these three models is most accurate at the moment? That’s easy to measure simply by filling in the actual numbers as we go. I added formulas to subtract the actual values from the forecasted values, day by day, across each model, so we can see which one proves most accurate. Here’s what the 2% model shows so far:
Clearly, the forecast is pretty far off and getting worse. In other words, 2% is too aggressive an assumption, thus January 26 is too early a date to expect herd immunity to be reached.
Let’s look, then, at the 1% model:
It’s also pretty far off, though a bit better than the 2% model. (Not long ago, it was farther off than the 2% model, so we can tell the rate of infection is declining.) The numbers are in red because they’re negative, meaning the model is too optimistic and is predicting fewer cases and deaths than we’re seeing. But they’re smaller numbers, indicating greater accuracy.
Here is the 1.5% forecast:
It’s a fair bit closer than either of the other two models, which isn’t surprising since the reported rate has been bouncing between 1% and 2% due to the rounding the website does. For that to happen, the actual rate would have to be somewhere in the middle.
Does this mean I should discard the 1% and 2% models? No, because the rate could swing in either direction from here. Over the next weeks and months as events unfold, I’ll probably add more tabs modeling other rates of infection if they do a better job. This gives us a way to contextualize the numbers we see each day. At some point if things are departing sufficiently from what we’ve observed since May 16, I might start over, basing the forecast on the number of cases as of that date (i.e., instead of the 1.48 million we had on May 16).
Over time, the model will change constantly, reflecting more and more new data and the effect that government policies and human behavior have on the spread of infection. If it turns out that fear, and not regulation, is driving social distancing behaviors, the rate might not go up by much. On the other hand, if people revolt and businesses start opening up again willy-nilly, the rate could skyrocket. These things cannot be predicted but their effect can be fed into the forecast.
So what I’ve created here is a model that says today, based on what is now known and what’s going on at this moment, I have a tentative herd immunity forecast date. As of May 24, I have at least some basis to believe that this pandemic will be over by April 20 of next year, after which the long, slow return to normal can begin. Notwithstanding the crudeness of my model, it gives me comfort just to have this projected date, vs. speculating endlessly about what could happen.
If this end date idea appeals to you too, I’m happy to share my spreadsheet … just drop me an email. Or, if you’re a lot better at such modeling than I am, I’d love to hear your comments and/or see your forecast. Or, if I have missed some all-important consideration and you’re able to shoot holes in my entire framework here, such that I discard it completely, I’d rather do that than stumble forward ignorantly, deceiving myself. (Will this post have been a totally wasted effort in that case? Mostly, yeah … but it’ll also be, arguably, an interesting historical testament to the kind of agonized cogitation this pandemic has brought about.)
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