Tag Archives: Pandemic

Simple Sims On Pandemic Variance

I’ve said it isn’t crazy to consider cutting pandemic deaths via more infection inequality, including via deliberate exposure. Some have said I’m evil to suggest that, while others have said it just can’t work. In this post, I address those latter doubts, by offering specific sim models wherein variance and deliberate exposure save lives. 

Of course, these models can’t prove that we should now adopt such policies. Every model makes specific assumptions that may not be true. The goal here is instead to show that that these ideas aren’t crazy. If they work and make sense in specific plausible situations, then we can’t dismiss them without knowing enough about our actual specific situation.

First, let me point you all to this Javascript sim model done by Zach Hess. He built this at my suggestion, but I haven’t yet learned enough Javascript to figure it all out. (Anyone want to translate it to pseudo-code?) It distinguishes 6 disease states: never-sick, exposed, recovered, asymptomatic sick, symptomatic sick, and in-intensive-care, and 3 kinds of workers: medical, critical, and general. It allows people to be put into quarantine.  

I think, but am not sure, that this model enforces a constraint on the total number of people who can fit into quarantine, and that having more available critical and medical workers makes sick folks less likely to die. Zack finds, for his default parameter values, that deliberately exposing & quarantining critical and medical workers early ends up saving lives. I presume he’s right. 

Over the last few days, I put together this simple spreadsheet model. (Feel free to copy, change, etc.) It doesn’t distinguish critical vs. medical vs. general workers, and so doesn’t capture gains from treating those differently. My baseline model starts with one contagious person in a US-sized population of 327M uninfected. 

After 7 days each contagious person becomes visibly sick, 10% of these sick need an average of 7 ICU days of help, and after 7 days some fraction of sick folks die, while the rest recover and become immune. Sick folks are added onto the usual 10K people who need ICU help each day, and their death rate goes as the logarithm of the daily total number of people who need ICU help. If only 10K people total need ICU help, only 0.4% of sick folks die, but if 50K per day people need ICU help, then 3% of them die.

The number of infected people who become contagious each day is proportional to the product of the uninfected count times the contagious count. Except that there is a quarantine that always holds 10M people, with a proportion of contagious vs. uninfected the same as the larger population. People in quarantine have only 2% of the usual rate of infecting others. The infection rate parameter is set so that, early on, the death so far count doubles about every 6 days. 

In that baseline mode, 14.3M people die within a year. The number of contagious peaks on day 168 and daily deaths peak on day 177, when 9.7% of sick folks die. I compare that baseline model with three variations. 

  1. Here, the infection rate is cut uniformly by 5%, from 1.0 to 0.95. As a result, 11.9M people die, with 16% fewer deaths than baseline. Contagious and deaths peak on days 195 and 205, and the peak death % is 9.2%.
  2. Here, instead of having one uniform population all with the same infection constant of 1.0, they are split into two initially equal-sized types, for whom these constants are 0.6 and 1.4. So while they together initially produce the same number of infected, one type gets infected 2.3 times as easily as the other type. In this variation, 10.4M people die, with 27% fewer deaths than baseline. Contagion and deaths peak on days 167 and 175, when the peak death % is 9.2%.
  3. Here, for the first 30 days 1.3M people per day are deliberately infected and then immediately placed into quarantine for 7 days until they get sick. They displace random people who would otherwise have been in quarantine. In this variation, 11.3M die, with 21% fewer deaths than baseline. The contagious count peaks on day 53, and deaths on day 40, when the death rate is 8.5%.

These simple models show that, to cut deaths, deliberate exposure can make sense, as can ways to cut infection rates and increase variance in who is more vs. less easily infected. For more details, these 3 graphs show # contagious, death % of sick, and # newly dead, all vs. days:

Of course there might be bugs in my spreadsheet; please do point them out.

Added 8am: Let me also note that in such simple models it does not help society to deliberately infect yourself, if once infected your chance of infecting others is the same as that of an average person who was infected accidentally. In that case you just pull all the curves forward in time a bit, and by increasing the rate of new sick folks slightly you increase their death rate slightly, and thus increase total deaths.

Added 09Mar: I found a small error in my spreadsheet, and so replaced the numbers and graphs above with corrected versions.

Added 17Mar: See more sims where select old or young to for deliberate exposure here.

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For Fast Escaped Pandemic, Max Infection Date Variance, Not Average

In an open column, … to provide greater dispersion, the vehicle distance varies from 50 to 100 meters, … distance between dismounted soldiers varies from 2 to 5 meters to allow for dispersion and space for marching comfort. (More)

The troop density has decreased through military history in proportion to the increase in lethality of weapons being use in combat. (More)

Armies moving in hostile areas usually spread out, as concentrations create attractive targets for enemy fire. For soldiers on foot, it might be possible to try to induce such dispersion by having a vicious wild animal chase them. After all, in the process of running fast to escape, they might spread out more than they otherwise might. But this would be crazy – there’s no reason to think this would induce just the right level of dispersion, and it would have many bad side effects. Better just to order soldiers to deliberately space the right distance. 

For a very infectious pandemic like COVID-19, clearly not contained and with no strong treatment likely soon, the fact that medical resources get overwhelmed toward a pandemic peak creates a big value in dispersion – spreading out infection dates. But, alas, our main method is that crazy “chased by a wild animal” approach, in this case chased by the virus itself. 

That is, each person tries to delay their infection as long as possible, in part via socially destructive acts like staying home instead of working. Like soldiers running from a wild animal, our varying efforts at delay do create some variance as a side effect. But probably less than optimal variance, and at great cost. 

Yes, delay has some value in allowing more stockpiling. For example, we should (but apparently aren’t) mass training more medical personnel who can function in makeshift ICU tents. But increasing average delay is can be less valuable than increasing delay variance. Even if we can’t just tell each person when to get infected, like telling soliders where to walk, we have several relevant policy levers. 

First, as I’ve discussed before, we might pay people to be deliberately exposed, and covering the cost of their medical treatment and quarantine until recovery. Yes, if their immunity has a limited duration, then we might want to not start deliberate exposure until there’s less than that duration before the pandemic peak. But there’s still big potential value here, especially via targeting medicine and critical infrastructure workers. 

Second, this is a situation were inequality of wealth, health, and social connections is good. In the last few years, many have loudly lamented many kinds of social inequalities that make the low feel ashamed and unloved, resulting in their more often becoming lonely and sick. Some are enough friends and money that they can afford go to all the parties, while others suffer in poverty alone. And no doubt many will cry loudly when such inequality makes the low get infected before the high.

But however bad such inequality might usually be, in a pandemic it is exactly what the doctor should order, if he could. Among a community close enough to share the same medical resources, the more that individuals vary in their likeliness of catching and passing on the pandemic, the better! Those who catch it early or late will do better than those who catch it just at the peak.  So for this pandemic, let’s maybe back off on whatever we now do to cut inequality, and maybe even open up more to whatever we are not doing that could increase inequality. 

In my next post, I’ll describe some simple concrete sim models supporting these claims.

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Deliberate Exposure Intuition

Many have expressed skepticism re my last post on controlled exposure. So let me see if I can’t communicate my intuition more clearly, so we can all examine it more carefully.

Assume we have a virus like COVID-19, highly infectious and substantially deadly, not blocked or cured by any known or soon-coming treatment. It takes up to 2+ weeks from exposure to death or recovery, and advanced medical resources like ICUs can cut death rates. Even with unusually strong quarantine efforts, COVID-19 currently seems to be escaping from its initial region and nation, doubling roughly every week. Even if that growth rate falls by a factor of three on average, it will reach most of the world within a year.

At which point roughly half of the world who isn’t immune gets infected over a perhaps two week period. Medical resources are completely overwhelmed, so ICUs save only a few. And the world economy takes a huge hit; for perhaps months before that point most workers have stayed home from work in an eventually futile effort to avoid exposure. At the worst possible moment, food, trash, cleaning, heating, and cooling may be scarce, increasing the fraction of sick who die.

To deal with this crisis, there are two key kinds of resources: medicine and isolation. With limited medical resources, including medical workers, we can treat the sick, and cut their chance of dying. We also have a limited set of quarantine resources, i.e., places where we can try to isolate people, places that vary in their health support and in their rate of infection leakage in and out. If we put the more likely infected into stronger isolation, that slows the disease spread.

Consider three different policy scenarios, based on three different policy priorities.

First, consider a policy that prioritizes immediate-treatment. This is a common priority in our medical systems today. Each day, medical and quarantine resources are devoted to the individuals for whom they seem most most-effective in keeping that person alive over the next few days. So hospital ICUs hold the patients whom ICUs can most help now. And the best quarantine locations are allocated to the apparently not-infected at most risk of dying if infected. (Such as the old.) Workers are allowed to stay home from work if they think that will increase personal safety.

In this scenario, medical and critical infrastructure workers may not be given priority in quarantines or medial treatment. So medical workers are culled earlier than others due to their extra contact with the sick, and most medical workers may be sick or stay home near the peak of the epidemic, which is a pretty sharp peak. Most workers in critical infrastructure may be home then too, and may have been there a while. Worse, by allocating isolation resources according to a risk of dying if infected, a treatment-focused policy does little to slow the disease spread.

Next, consider a policy that more prioritizes containment. This is the usual priority of public health today facing a new contagious disease. Here more people become more isolated, and the best isolation resources are allocated much more to those most likely to be recently infected, not to those most likely to die if infected. Efforts may be made here to isolate medical workers, even if that results in worse individual treatment.

This priority can make sense given a substantial chance that the disease can be stopped from spreading beyond an initial area. Even if spread seems inevitable eventually, a containment priority also makes sense if that policy makes an effective treatment substantially more likely to be found before this disease spreads to most everyone. Or if more medical or isolation resources can be created in the extra time. Hope springs eternal, and it feels good to assume the best and act on hope.

But what if there is little hope of containing or treating the disease before most everyone is exposed? And what if getting sick and then recovering often gives someone substantial immunity to the disease for a period? After all, if everyone is constantly exposed, the recovered quickly get sick again, and this infection has high mortality, then death is coming soon no matter what. So we must hope for some immunity.

For this situation, consider a policy that prioritizes long-term treatment-resources. Most everyone will be exposed within a year or so, and unless they are immune they will get sick, at which point their chance of recovery instead of death should depend on medical resources, and critical infrastructure, at that time. So this policy seeks to create a pattern of isolation, and possibly deliberate exposure, to increase the average resources available to help people recover when they are sick.

The obvious problem here is that the above scenarios can have a pretty sharp peak in infection rates, overwhelming medical resources at that point in time. And workers who stay home also threaten the availability of other critical infrastructure resources. Yes, if containment slows the rate of growth of the disease, it also spreads out the time period of peak infection by a similar factor. But that could still be pretty short period.

Relative to the containment policy, this long term resource policy would seek to move the time of infection of many people from near the peak, to substantially earlier than the peak. Moving to later than the peak is not possible, if we’ve been containing as much as possible. And the obvious way to infect people earlier is to directly expose them, on purpose.

Of course directly exposing people won’t help spread out the peak if the people exposed are isolated to the same average degree as people are in the containment scenario. That would instead just move the peak to an earlier point in time, and perhaps even make it sharper, by making the disease spread faster. So this long-term treatment policy would have to involve infecting some people deliberately, while giving them much higher than average quality isolation. If their isolation were very good, then they’d use medical resources at an earlier point in time when such resources are more available, without adding much to the overall growth of the disease.

Now, if good isolation resources, and medical resources, were already strained dealing with a flux of likely infected from outside, then there might be little point in adding new infected on purpose. But what if there are many good isolated places available not being fully used to deal with folks very likely to have been exposed, and also available medical resources not fully used, what if recovered folks had little risk of infecting others for a period, and what if we were closer in time to the peak than that average period between reinfections? Well that’s when we might tempted to deliberately expose some, and then to strongly isolate them.

One key idea here is to create a stronger correlation between the strength of isolation of a place and the likelihood that people there are infected. Such a strong correlation allows us to create a population of already recovered folks who are at least temporarily immune. And that can spread out the period of peak infection, so that more medical resources are available to treat the sick. And that can cut the average mortality rate, which means that more people don’t die.

People who work in medicine and critical infrastructure seem especially promising candidates for early deliberate exposure. This is because after recovery they become more available to work during the peak infection period. They are not sick then, and are less afraid of being exposed then, making it easier to persuade them to go to work. The other set of promising candidates are those most likely to die without sufficient help, which seems to be men and especially the old.

And that’s the intuition behind deliberate exposure. Its wisdom depends on some parameters of which we are unsure, and may learn more about soon. So it seems clearer that we should think more about such options than that we should pull the trigger to start one now. And there are substantial challenges in organizing such a policy fast enough, and in gaining sufficient public and elite support to allow it. Maybe this can’t work this time, and must wait until another big pandemic.

But contrary to many loud and rude commenters lately, this option isn’t crazy. And within the next year we may come to see and suffer the full consequences of not working harder to spread out a pandemic peak of maximum infection and medical need.

Added 2p: The obvious easy win policy solution (given that key assumptions hold) here is just to make it easy for people to volunteer for (1) exposure to virus, (2) strong 24 day quarantine, (3) medical help while there, (4) regular checkups afterward. Create a place where people can go to do this, an easy way to sign up legally, and pay to expose and house them there. Maybe even pay them extra if they work in medicine or critical infrastructure. (Btw, as such an option isn’t now available, and I don’t work in critical infrastructure, it wouldn’t help society much for me to just “go infect yourself”, as many have suggested in so many colorful ways. And as I don’t own my family, I can’t volunteer them.)

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Consider Controlled Infection

In many places long ago, in families with many kids, as soon as one kid caught an illness, parents would put the other kids in close contact, so they could all catch it at once. Because it was less trouble to care for all the kids in a family at once than to care for them one at a time.

Should we also consider controlled infection to deal with our current pandemic? Like controlled burns that prevent later larger fires, it might be a good idea to expose some people early on purpose.

Today a coronavirus is spreading rapidly across China, and the world, and many are trying hard to resist that spread. One obvious reason to resist is the hope that the spread can be completely stopped, limiting how many are exposed. However, once a contagious enough virus has spread to enough people and places, this scenario becomes quite unlikely; the virus will soon spread to most everywhere that isn’t high isolated.

Unfortunately, we are probably already past this point of no return with coronavirus. It seems to spread easily, apparently including via people who are contagious but don’t show symptoms. It already seems to have spread from its initial region to infect many people in a great many other Chinese cities and regions (thousands infected, dozens dead). And that’s with keeping everyone home from work, which can’t last much longer. Once this virus comes to infect most of China, it seems hard to imagine a strong enough China wall (a 24-day quarantine for everyone leaving) to keep it from spreading further. Especially since China & WHO are arguing against such a wall, and we already have confirmed a few hundred cases outside China; they’ve doubled every week for four weeks.

Another reason to resist virus spread is in the hope that a vaccine (or other effective treatment) will be available before it spreads everywhere, stopping the spread at that point. There’s some hope for a drug soon to prevent infections, but the odds are poor and if that doesn’t work prospects are dim. Alas “typically, making a new vaccine takes a decade or longer”, and estimates for this case are at least 18 months. That doesn’t include time to manufacture and distribute it, once we know how to make it.

As of yesterday, total known deaths were 1384, a number that’s had a 6 day doubling time lately. (A very different method estimates 7 day doubling.) At that rate, in four months deaths go up by a factor of a million, which is basically the whole planet. So unless long-term growth rates slow by more than a factor of four, there’s probably not time for a vaccine to save us.

If the virus spreads to most of the world, so most everyone is exposed, then the fraction of the world that dies depends how deadly is the virus, which we just don’t know, and can’t control. Maybe we’ll get lucky, and this one isn’t much worse than influenza. But we are probably not so lucky. The fraction of the world that dies also depends our systems of social support, which we can do more to influence.

I’m not a medical professional, so I can’t speak much to medical issues. But I am an economist, so I can speak to social support issues. I see two big potential problems. One is that our medical systems have limited capacities, especially for intensive care. So if everyone gets sick in the same week or two, not only won’t the vast majority get much of help from hospitals, they may not even be able to get much help from each other, such as via cleaning and feeding. Perhaps greatly increasing death rates. This problem might be cut if we spread out the infection out over time, so that different people were sick at different times.

The other related problem is where many non-sick people stay away from work to avoid getting sick. If enough people do this, especially at critical infrastructure jobs, then the whole economy may collapse. And not only is a collapsed economy bad for most everyone, sick people do much worse there. Not only can’t they get to a doctor or hospital, they might not even be able to get food or heating/cooling. Infected surfaces don’t get cleaned, and maybe even dead bodies don’t get removed. Thieves don’t get stopped. And so on. We can already see social support partially collapsing in Wuhan now, and it’s not pretty.

There’s an obvious, if disturbing, solution here: controlled exposure. We could not only insist that critical workers go to work, but we might also choose on purpose who gets exposed when. We can’t slow down infection very much, but we can speed it up a lot, via deliberately exposing particular people at particular times, according to a plan.

Such a plan shouldn’t just expose random people early, as they’d be likely to infect others around them. Instead, groups might be taken together to isolated places to be exposed, or maybe whole city blocks could be isolated and then exposed at once. Exposed groups should be kept strongly isolated from others until they are not longer very infectious.

Those who work in critical infrastructure, especially medicine, are ideal candidates to go early. Such a plan should only expose a small fraction of each critical workforce at any one time, so that most of them remain available to keep the lights on. If critical workers could be moved around fast enough, perhaps different cities could be exposed at different times, with critical workers moving to each new city to be ready to keep services working there.

Such plans can help even if some people who are infected and recover can get reinfected later. As long as being infected gives enough people enough immunity for a long enough time period, that is enough for this plan to spread out the infections over a time period of similar duration, so medical service needs don’t all appear together. Even an immunity of only two months, which is extremely short compared to most diseases, would allow a lot of spreading.

People selected to be exposed earlier might be paid extra cash, to compensate for perceived extra risk. (Maybe X days worth of their usual wages, so as not to especially select the poor.) Or perhaps they could be paid in extra priority for sick associates if medical help is rationed later. (I’d seriously consider both kinds of offers.) We might even be able to implement a whole plan like this entirely via volunteers, though adding that constraint may make a strong plan harder to design. A compromise might be to let city blocks vote on if to be paid to go early together. I’m willing to help in design work on this, if that could help make the difference.

I don’t have a detailed plans to offer, and obviously any such plans should be considered very carefully. Also obviously, such plans might face strong opposition, which could undermine them. If they were designed or implemented badly, they might even make things worse. But the alternative is to risk having large fractions of the population get sick at once, while the economy collapses due to critical workers staying home to avoid getting sick. A scenario which could end up a lot worse.

So authorities, and the rest of us, should at least consider controlled infection as a future option. I’m not saying we should start such a plan now; maybe that drug will work, and it will all be over soon. But if not, we should start to ask when we might learn what could help us decide, what might be a good time to pull the trigger on such a plan, and how to prepare earlier for the possibility of wanting to pull such a trigger later.

Added 17Feb: See also my next post elaborating the intuition behind why and when deliberate exposure could make sense.

Added 03Mar: See also my spreadsheet model, and further discussion.

Added 15Mar: See also elaborations of spreadsheet model.

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