Guest Post by Husband Scientist Frank Sanders
Stand back, everybody; I’m a professional scientist and I’m here to tell you what you need to know, in an optimistically upbeat way, about Covid-19 transmission and how to stop it! (Or at least how to cool its jets quite a bit.)
I’m going to tell you what the government should be telling you, but for some reason hasn’t quite seemed to be getting out to everybody.
In the Beginning…
For starters, suppose you have a big, empty, open-mouthed jar and some spare time on your hands. Starting at noon you drop a grain of sand into it. One minute later, at 12:01, you drop in two grains. A minute after that, at 12:02, you drop in four grains. Then eight grains at 12:03. And 16 grains at 12:04. And so on. The jar gradually fills as you drop in sand grains every minute, always doubling the number of grains that you drop in at each one-minute interval. Eventually, the jar is completely full at midnight.
(The total number of sand grains in this thought-experiment would ultimately exceed the number of protons in the Universe. But hey, let’s imagine it’s a really, really big jar, OK?)
- When was the jar one-quarter full?
- When was it half-full?
- At 11:58 PM, two minutes before midnight, the jar was ¼ full.
- At 11:59 PM, one minute before midnight, it was ½ full.
The weird way our jar fills up is called exponential growth. When something grows exponentially it goes very slowly at first, barely creeping along. Not even noticeable. And then all of a sudden, before you know it, the thing that’s been so slowly growing for a long time is all over you, like a swarm of giant ravenous radioactive ants overrunning a city in a 1950s monster movie. And now the Army can’t stop ‘em!
But I digress…
Pass It On, Brother
When a new disease bursts into a host population that has no prior immunity, it begins to spread in the same way as our jar fills with exponential sand. One person has it at the start (we’ll imagine). That person in turn gives it to some number of additional people. We’ll call that pass-on number ‘R0’ (voiced “R-nought,” short-hand for the disease’s basic reproduction rate from one person to the next). Then each of those second-tier R0 people gives it to R0 more people in a third tier, and so on. (The thing being that we don’t increase by adding people from one tier to the next, we increase by multiplying people at each stage. That’s crucially important to understand. You’ll see…)
For measles the spreading-rate reproduction number R0 is a whopping 13, making measles the most contagious of known diseases. For measles the number of people who have it at each step of reproduction (each stage of the process) is: 1; 13; 132 = 169; 133 = 2197; 134 = 28,560; and so on. Yow! That math is why public health officials practically poop their pants when they know that measles has broken out somewhere.
For our new disease that’s burst onto the world scene (COrona VIrus Disease of 2019, or Covid-19), R0 is around 2.5. That means each infected person will on average pass it on to 2 or 3 other people, if left to their own devices. (More on that below.)
The number of people expected to develop Covid-19 at each reproduction stage is: 1; 2.5; 2.52 = 6.25; 2.53 = about 16; 2.54 = about 39; 2.55 = about 98; and so on. It’s not as bad as measles but it’s still an alarmingly steep rate of natural increase.
To give this some perspective, the Covid-19 R0 rate is comparable to atoms splitting in the chain reaction of an atomic bomb. Like multiplying neutrons that split atoms in an ever-increasing cascade in a ball of uranium or plutonium, an R0 of 2.5 can make a pretty big epidemiological bang; it will definitely sustain a serious regional epidemic or even a global pandemic.
As another point of perspective, R0 for flu runs between 1.1 to 1.5; Covid-19 is roughly twice as transmissible as flu. Covid-19’s basic transmission rate is seriously high; it should therefore not be toyed with or underestimated, despite some people’s claims to the contrary.
Corollary (Had to Get that Word in Here Somewhere)
The corollary to exponential growth is that the true number of cases will constantly (and always) exceed the number that are known from testing. This because the testing rate can’t keep up with the multiplication rate of the cases. The problem has been exacerbated in America by a severe lack of test kits. It’s been a public mystery as to why and how that shortage has occurred. Ordinarily the CDC is all over this sort of thing. Anyway it means that we can draw no comfort from a low number of known cases. The testing fiasco means that the known cases form the very small tip of what is surely by now a very large iceberg.
It would be useful to test thousands of people at random to see how many come up positive in the general population. That would allow us to get a better handle on the disease’s true rate of incidence in the population and thus better understand where it’s going epidemiologically. But the testing situation has now become such a debacle, and now we’re so far behind the testing curve, that widespread general testing clearly isn’t going to happen. So let’s be realistic and move on.
It appears that the time interval required for the number of Covid-19 cases to double is between four to seven days. For simplicity let’s split the difference and call the Covid-19 doubling time five days.
Here’s what that means: On Day Zero there is one case. On Day 5 there will be two cases. On Day 10 there will be four cases. On Day 15 there will be eight cases, and so on, doubling every five days in just the same way as we were doubling the grains of sand into our jar once every minute.
At that rate, a doubling of cases every five days, one million people would be infected within 100 calendar days, basically just three months.
In 135 to 136 calendar days, a mere four and a half months, the total number of people who had been infected would be in the ballpark of 200 million, which is about 60 percent of the US population. Most of those cases would occur near the end of that interval, per the jar that we filled exponentially.
(Disclaimer from Bob over in Legal: This is a bit of a simplification of how the actual exponential growth would occur. It illustrates however the essentials of the manner and scale of growth for R0 = 2.5.)
Take it to the Limit
Of course there’s a limit to the total number of people who are likely to ever become infected. This is because as more and more people become first infected and then immune to subsequent re-infection (which is what happens with viruses), the little bug that’s been spreading wildly and partying non-stop starts running into people who’ve gained immunity and therefore has difficulty in moving on to new victims. Bad for the bug but good for the remaining population of potential victims. Even for killer viruses the party always comes to an end, eventually. The only question is when and how.
That limiting number of people who are likely to be infected is governed not by prayer but by math and physics, just like your car’s ignition system. It turns out to be a simple function of R0. (Notice how I threw in the word “simple” to make that sentence about math more friendly.)
Specifically, the percentage of the total population that is likely to become infected by a disease outbreak is (1 – (1/ R0)). Once that percentage of people has gained immunity (the hard way, unfortunately), a disease’s spread mostly grinds to a halt.
This little bit of math pays big dividends for disease planners, whose jobs are even more stressful than wedding planners. It tells us that if R0 = 1 (where each infected person only infects one other person), then we get a total overall incidence of (1 – (1/1)) = (1 – 1) = 0.
If R0 = 1 then the disease doesn’t go anywhere. Whew! Epidemic disaster averted! We’ll return to this factoid shortly.
If R0 = 1.3, consistent with flu, then the infected total can go as high as (1 – (1/1.3) = 23 percent of the population. That’s nearly one person in every four. Which is about right for flu season if a lot of people don’t get vaccinated. (Vaccinations reduce R0. In fact the entire public-health goal of vaccination programs is to get R0 down to 1 or less in a targeted population, to terminate disease spread in that population.)
For R0 = 13 for measles, then the percentage we get for an unvaccinated population is an astounding 92 percent. See above where I said that measles outbreaks make public health officials poop their pants. That’s why measles vaccinations are so crucially important. (The corollary is that in order to be effective in stopping the spread of measles, about 92 percent of a population needs to be vaccinated.)
For Covid-19, putting R0 = 2.5 into our equation gives us a total possible infection rate of as much as 60 percent of the American population. Although the actual number will likely be lower for a variety of reasons, this tells us how seriously we should take this disease. Which is to say, very seriously. It’s not a joke and it’s not the flu. It’s a public health crisis. People who try to claim otherwise should wise up and get with the program (and the math).
First the Bad News
Now do you see why, up above, I looked at how long it would take to infect 200 million people given the doubling time for Covid-19 of five days? It’s because 60 percent of the American people, the theoretical limit for how many people could contract the illness, is about 200 million souls.
So here’s the deal: If Covid-19 explodes into a population with no pre-existing immunity (which is true for all of humanity right now), and its R0 is about 2.5 (which is pretty confidently known), and its doubling interval is about five days (also pretty well known at this point), then the outbreak will infect as many as 200 million Americans before it self-limits. And the time required to get there is as short as a scant four and a half months.
The fatality rate for Covid-19 looks like it’s somewhere between 1 percent and 3 percent of those who are infected. Think that doesn’t sound so bad? Think again.
For comparison, the death rate for flu varies but tends to be about 0.1 percent (one person dead for every thousand who contract the illness). The Covid-19 death rate, at one to three percent (10 to 30 fatalities for every 1,000 cases), is therefore somewhere between ten and thirty times higher than for flu. If the theoretical maximum number (200 million) of Americans actually were to get the illness, then the total number of American Covid-19 deaths would be expected to run between two million to six million people. That would be horrendous. Even if the full impact were somewhat lower, can you imagine the impact of even one million people dying of this thing in the space of a few months?
When the House Wins the Game
Or let’s think about it this way: You’re forced to play a gambling game (there’s a gun being held to your head) in which there is a spinning roulette-style wheel with 100 slots. 97 of those slots are green and three are black. A marble with your name on it is tossed into the track on the outside of the wheel while the wheel spins. Everything is in motion until the ball falls out of the track and into one of the hundred slots. If it hits any of the 97 green slots you live and if it hits one of the three black slot you die.
Do you really want to play that game? Me neither.
There’s another problem with this unimpeded spreading scenario, if it were to come true: We would have 200 million cases of the illness all hitting hospitals and clinics in a very short period, just four and a half months. And most of those cases would strike just at the end of that period (like the grains exponentially filled the jar, which was half-full at only one minute remaining before midnight).
Health facilities, health care workers, everybody and everything, would be totally overwhelmed. Which would push the death rate sharply upward. Clinics would be forced to triage for who would live and who would die. Nobody wants that.
What Will Work and What Won’t
What can we do?
First, I’ll tell you what won’t help, in order to clear unhelpful ideas out of the way first. Then I’ll tell you what will work.
What Won’t Help (at Least Not Much):
- Only isolating or quarantining people who are visibly ill with Covid-19 won’t stop the spread, in itself. The reason is that this nasty little bug moves from a first person to a second person before the first person shows any symptoms. The first person spreads it before they are aware that they have it themselves. (One reason that a related illness, SARS, was mostly stopped in its tracks was that it only becomes transmissible after an infected person shows symptoms. Covid-19 hasn’t made that mistake and as a result it’s gone Global Platinum.) On top of that, many people infected with Covid-19 never show any symptoms, or they get such mild symptoms that they never even know they’ve had it. But they nevertheless spread the virus to others while their immune systems are fighting it off. Mind you, I’m not saying that people who are ill shouldn’t be isolated or quarantined; isolation is helpful and should be implemented for those who are ill or may have been exposed. I’m just saying that only isolating or quarantining people with symptoms won’t, in and of itself, stop the illness’s spread.
- Stopping all movements of people across boundaries (of countries, states, counties, cities or what have you) will be generally unhelpful. This seems counterintuitive, so let me explain. Suppose a given population of uninfected people is 100 percent isolated from an infected population, by a line drawn between them. That expedient would actually protect the uninfected population. But that goal is simply impossible. Sooner or later, one way or the other, somebody who’s infected is going to cross that boundary line and enter the uninfected population. When they do, they will become Case Zero and the inexorable, exponential-growth math of R0 will begin. Once the previously uninfected population gets a significant number of home-grown infections going, stopping further movements between the two populations won’t do much (if any) good. (I will say, though, that at the very beginning of an outbreak some restrictions on movements can buy time for health responders to prepare for the outbreak that’s barreling toward them.)
- Stopping movements across boundaries (screening at borders) for people who are showing visible symptoms is generally not going to be effective, either, for Covid-19. As mentioned above, lots of people are asymptomatic throughout their illness and transmit it regardless of that. Others are eventually symptomatic but are still in their asymptomatic incubation period when they are still transmitting the virus. The only way to get around this problem is to use a clinical test to screen every single person arriving from a population where the disease is present. In the modern age of jet travel, with millions of people moving around every day, that amount of screening is impossible. Not to mention that it takes at least 72 hours to get a turn-around on a test result. Right now, we can’t even test many of our sick people who are already streaming into clinics. We certainly can’t do test screening for millions of travelers every day.
- Closing schools might help a little. But thankfully it appears that children aren’t very susceptible to Covid-19 infection. So maybe we should put a pin in that one, noting that school closings are better than nothing but that in and of themselves they won’t get us to where we need to be.
Now the Good News (At Last)
OK, you say, if none of those things does much good, what can we do? It turns out we can do quite a bit, and one thing in particular, to mitigate the math and therefore the disease.
We can reduce R0!!
Instead of each infected person infecting 2.5 additional people, we need to reduce the transmission rate down to R0 = 1 or less, or something close to that.
Why? Just look back, up near the top of this piece. Remember where we saw that if R0 = 1 (or less), then the previously unbreakable chain-reaction breaks down and the total remaining population that gets infected goes to zero? That’s what we have to do.
And we can do it.
Scrub, Scrub, Scrub, Scrub Your Hands (To be Sung to the Tune of Shake, Shake, Shake, Shake Your Booty)
The way we do it is multi-pronged. First and foremost, we’ve really got to be washing our hands at every opportunity, so as to stop depositing the virus particles on surfaces, and to kill any virus particles on our skin (that skin usually being on our hands).
Using plain soap and water is idiotically simple, yet highly effective. (This where you can feel free to spontaneously blurt out, Leapin’ Lizards, Mr. Science!)
It’s just like when the magnificent Florence Nightingale and her truly heroic nurses saved the lives of tens of thousands of British soldiers in the Crimean War by applying plain soap and water to their wounds and their living quarters (and making them eat fresh-grown vegetables). Her work was met by total chagrin from a bunch of burly bearded British generals who grumped and griped and went Harrumph. They screamed and cried about how nobody could afford any of that and how unfair and un-Godly it was to force the soldiers to wash themselves and eat greens. But when Queen Victoria read about the women’s accomplishments in the Times and then backed them up with hearty public congratulations, nobody was about to argue with her. (I digress again. Look it up—it’ll be worth your while.)
Unlike some diseases, this virus has a super-simple business model for spreading from person to person: By getting into our eyes, noses and mouths. The way it gets there is either by exposure to airborne aerosols from infected people who are coughing, or else by getting put in there by riding on our own hands when we touch our eyes, noses and mouths.
Hand washing cuts off the virus’s touching route.
Not touching your face is good, too. But let’s stay real here.
Hi There, St. Simeon Stylites (Look Him Up. Or Rather, Look Up at Him)
I’m not saying we should start lives living on the tops of pillars in the desert for decades on end like some guys used to do. But reasonably self-isolating ourselves if we know we are infected, or if we have been exposed to so someone who’s infected, absolutely cuts off the virus’s second route, which is airborne aerosols from people’s coughs. It shuts down all the flights of Air Covid.
However, you will say (if you’ve been paying attention), what about that stuff about asymptomatic people spreading it?
Well, I answer, you’re right. And that’s why, right now, we all need to self-isolate ourselves as much as we reasonably can.
By self-isolating even if we don’t imagine we’ve got this bug, we do two things:
- We reduce the chances that we encounter the virus from other people who have it but don’t know it.
- We reduce the chances that we pass the virus to others because we ourselves already have it but don’t know it.
Self-isolating, which means not going to work, not gathering in large crowds, and generally just limiting contact with others to the bare minimum, will reduce R0. Even if we don’t get to the ideal level of R0 = 1 or less, merely knocking R0 down somewhat will do two incredibly terrific things:
- It will reduce the overall number of people who will finally become infected (remember that little equation from above).
- It will slow down the disease’s growth in the population and thus greatly stretch out the calendar interval during which the illness spreads.
These two bullets are critically important. Suppose that we reduce R0 to 1.3, the same as flu. Then, as we saw above, only 23 percent of the population gets sick, in total. And the doubling time goes up, to maybe 10 days. The result is that 77 million people get sick and it takes a year for those cases to evolve. That’s still a first-class emergency but it’s way better than the first scenario. (In the disaster-management business, you have to take what you can get for ‘better.’)
If we can achieve the holy grail of R0 = 1 or less, then this thing will be stopped in its tracks.
It just can’t be stressed too much: We all need to self-isolate as much as we can right now, and we all need to really wash our hands. That will save lives. Lots of lives.
Strike Your Blow
Strike your own blow for humanity! Wash your hands! And stay home as much as you can.
My own motto is: Do your part to cut R-nought!!
I won’t sugar-coat it. This is a very serious problem, a terrible situation. A lot of people are going to die. Hell, I could die just like anybody else, and I’ve gotta say that I’m very disappointed by that factoid. But we can all do our part to help. We can help ourselves and others by doing just the two simple things of using soap and water and self-isolating.
Economic hardship? Money being lost? Hell yes. No getting around it. This outbreak will, as they say, slow down the economy. We absolutely need to do what we can to mitigate the financial and physical hardships of our fellows. Unfortunately, though, it’s the price (literally) that’s going to have to be paid.
Warmer summer weather? It might reduce R0 somewhat. But unless warmer weather gets R0 down to 1, it won’t stop the disease. Even if R0 does go down in the summer it will likely bounce back up again in the fall. That’s what the 1918 flu pandemic did between the spring and the fall of that year. It’s OK if it happens but it’s not a real solution and it’s not a plan. Hoping is not planning.
For How Long?
The government and the media have not made it clear that this is not a short-term issue. That’s a sad failure in messaging.
This is going to be a long-haul problem. I’ll say that again: This is going to go on for a long, long time. Just like the movie The English Patient but (arguably) worse. Like a year or more, although the most acute stage(s) should come sooner than later.
The way we can expect this to go is: First it will get really bad (exponential growth). Then it will ease up some. Then it will get bad again, albeit not as bad as the first go-around. And so on in an oscillatory fashion until there’s a vaccine that becomes generally available maybe a year or two from now.
If you’ve gotten through this discussion and you’ve absorbed it, congratulations. You now know as much about this as any of our public health officials. And way, way more than our President.