# The math on the cost of infecting people

What if you give somebody a disease that harms them? It is legal to sue over this, and to have wrongful death lawsuits by the survivors. Wrongful death lawsuits, according to one recent North Carolina study, fetched about \$1.4M on average, though they are going to vary a lot. They combine lost income with pain and suffering by the survivors. While wrongful death lawsuits are done after-the-fact, if you considered them taking place before the death (as they sometimes did with AIDS.) Indeed, the general statistical value put on a human life by policymakers is around \$10M, no matter what the age.

## Cost of deaths

Costing human lives is always complex, particularly when you describe hypothetical activities which will take them. For many people, the amount of money you would need to pay them to get advance consent to risk their lives is much higher than these statistical values. Some people would accept \$100,000 to let you put their life 1% at risk, others would have a higher price. Some are rich enough that there is no amount they would accept.

But to make it simple, let's work on the lower end of the spectrum at \$1M, and let's use today's commonly estimated infection fatality rate of 1% -- lower than the 3.5% that the WHO published at the time that policymakers were deciding lockdowns.

This means that infecting somebody should have a mean cost of at least \$10,000, just for the death risk. However, infecting them also puts them at much higher risk for at least 2 painful weeks of downtime, and loss of work, or in cases with light symptoms, just the 2 weeks of isolation and loss of work. You need to add about \$5,000 for that. Some decent fraction of those infected might need hospitalization, which could cost tens of thousands extra -- I have not factored this in, and in the current world this is paid by health insurance, but in this hypothetical world the insurance company would go after the infector for the costs.

Wrongful death suits don't include money to make up for the death itself, as that can't be remedied and the dead can't sue. Criminal law deals with that. The fatally ill can sue, but not in a way as to get remedy before they die.

### Cost of downstream infections

The problem is that infecting one person isn't where it ends. Your infectee is going to spread secondary infections, and they are going to spread more, and so on, and so on, until the outbreak ends.

You are certainly at least partly responsible for those they infect. One can argue it would not have happened at all without you. Some of them will also do things they shouldn't, and bear some responsibility, and share the liability with you. Each case would be different -- the symptomatic infectee who went to a cuddle party bears a lot more share of responsibility than the cautious one who sheltered at home but touched a handrail while shopping. As before though, we want to figure a mean, which will be more the result of policy and precedent. For a simple model, let's consider a 50-50 split, with you being responsible for 1/2 of the costs of those you infect, and your infector responsible for the rest. As such, you are responsible as well for 25% of the costs of those infected by your infectees and so on.

Now you can project a number. Estimates for the R0 of SARS-Cov2 range from around 3 to 6 in a non-locked-down world. Let's go with the lower bound of 3.

Put it all together and the average infected person will infect 3, with a cost of \$15,000 or a total of \$45,000 from just those three. However, they will infect others. How many is hard to calculate. If you are "patient 0" at the start of an epidemic, then you will be responsible for the whole population. The number downstream from you is going to depend on what fraction of the population is left to be infected (today that's well over 90%) and how many other people are, like you, not social distancing.

If there are 10,000 not social distancing infected in a country of 300M people like the USA, and it goes on until herd immunity with 250M infected and 2.5M dead, then on an even basis, each of the 10,000 will, on average, be responsible for 25,000 infections and 250 fatalities. (This is a great oversimplification because some of those who are keeping locked down will still infect a few, but we can use it for this back of envelope analysis.) That's about 8 or 9 generations at R0 of 3.

Here's a breakdown of how that works. You will infect 3 people. Each of them is owed \$15,000, for a total of \$45,000. But half of that -- \$22,500 is owed by the person who infected you. (Who will in turn be owed have of that by their infector.)

Your 3 infectees will infect 3 each, for 9 grand-infectees of yours. Again, they each deserve \$15K, but you are responsible for only 1/4 of that, adding on average \$34K. Next generation has 27 infectees for which you owe only 1/8th and so on. By the time we get to generation 8, there are 6,500 infectees but you owe only 1/256th of their total liability -- about \$400K. It keeps growing in this exponential way until herd immunity (or a lockdown) slows the growth.

The last variable we must add is the probability that, if you go out and socialize, you will get infected. Most estimates suggest that's pretty high in a non-locked down world. The only question is whether it happens sooner (when you will then contribute to the infection of many) or later, as the herd immunity approaches. But if you accept a 5% chance of getting infected fairly early on, your expected cost just for going outside runs about \$50,000. And about 9 manslaughter charges on average. But with that number, it means the risk you take by being an early-adopter of non-locked down life is about \$50,000, and about 9 possible homicide/manslaughter chargers.

It's not like you step outside and it costs you \$50K and a homicide rap. Some poeple would go out and infect nobody, or do it very late. Others would infect and kill an above average number of people. It would be a big gamble, though of course it is one you control since you can control how much you socialize. Protestors want to socialize almost like 2019, going to restaurants, movies, jobs, sporting events. The real cost you would end up responsible for would range from nothing to many millions.

## Insurance

When you have that much range of risk, the answer is to buy insurance, at least for the financial risk. But the insurance companies are going to want a premium of probably double the average liability -- which is to say, in this calculation, of about \$100,000.

Are you ready to pay that premium? Or just take the risk of losing the \$millions? Do you even have the \$millions to pay? Of course, even if you can afford that, if the criminal charges come to bear, not even a billionaire can afford them.

Which means, you're going to lock down, even if it means losing a lot of money. Even without the jail time. Sure, you will argue that those people who died would have got it some other way if not via you, but it will be you that did it. And with all the press, nobody can argue you didn't know better. Especially if you were in a protest march, defying the advice to lockdown.

You can play with the numbers. As R0 goes up, your liability risk becomes much higher if you get infected early, and lower if you do it later. If R0 hits the magic number of 2 (which is to say, the reciprocal of the portion of the liability passed on to the person who infected you) the cost is no longer exponential and becomes flat, but still equal to about \$300,000 if you get infected and a more tolerable \$15,000 if you take a 5% risk of getting infected. The risk of killing is still very high.

If your infector takes less than half the liability for downstream infections, you can slow it down. If they take more than half (which many would argue is reasonable because the infections don't happen without them,) it speeds up.

The core reality is this -- an exponential number of people get infected (or dead) thanks to you, and if you take your responsibility for it in any serious way, the cost is immense. So high that you won't need any law to tell you to lock down, to close your business, to abandon your job, and to shelter in place.

## Criminal charges

Get R0 down (with a lockdown) and suddenly the disease dies out with time rather than growing to herd immunity. Your cost is much more reasonable. In addition, if you did everything reasonable to avoid infecting others, chances are you would not be guilty of negligent homicide.

Homicide and manslaughter, however, are very different from civil liability. They can't are not "split up" so that if your secondary infectee dies, you and the intermediary each get charged with "half a homicide." When two people participate in a homicide, they both get a homicide charge, even if one is much more culpable than the other. (There can also be conspiracy charges for groups.) The concept of 8 people in a chain being responsible for a homicide is of course untested. Certainly in a deliberate homicide (where a client pays a mob boss for a hit, and the boss gives it to a subordinate who gives it to a hit man) all would be guilty of murder-for-hire and probably consiracy. It's clear clear when the killing is negligent rather than intentional, or not even willful. (Those who are not social distancing today, however, are aware they are not doing it and that it is a risky activity for them and others.)

Some may wonder, "But Don't I get a payment from my own infector to balance this?" You do, but that payment is not to balance you for that. Rather it would or should be to compensate for the actual hardships you got for being infected. If you got no symptoms, it would only cover your cost of quarantine -- if you knew to do that. If you got hospitalized you would get more, but you suffered a terrible cost, so it's not a profit for you, unless there are punitive damages added.

This number gets further complication if some liability is given to those who facilitated the breeding and transmission of the disease, namely those who operated venues and events where people congregated, particularly when they did so knowing the risk. If I get Covid from somebody who attended a tightly packed church in spite of all warnings of the risk of that, one can argue that my infector, their infector and the church all play a role and have a share of liability.

It's hard to say what share of liability they would get. If it's a very large share it actually would diminish the cost to individuals. But it does not have to be a very large share before it scares the venues and events, and their insurance companies. This is particularly true in the world of deep pocket lawsuits, where such parties are more prone to being sued, though I am hypothesizing a world where we can actually find all the liable parties. Even in that world, the deep pocketed parties would pay more because some of the individuals would not have financial means to pay the remedy.

As such, you would find that most businesses, venues and events would be unable to get insurance of any kind if they didn't shut down. If they could buy insurance that excluded Covid liability they could afford that, but they would have to face that liability on themselves -- possibly low if there is minimal infection at their event, but quite possibly catastrophic and business-ending. They'll shut down.

## Comments

### If social distancing works...

If there are 10,000 not social distancing infected in a country of 300M people like the USA, and it goes on until herd immunity with 250M infected and 2.5M dead, then on an even basis, each of the 10,000 will, on average, be responsible for 25,000 infections and 250 fatalities.

How do the 299,990,000 people who are social distancing get it?

Those numbers are completely impossible.

Now, if there are 250,000,000 people not social distancing (in a country with 300,000,000), and it goes on until herd immunity with 250M infected and 2.5M dead, then, on an even basis, each of the 250,000,000 will, on average, be responsible for 1 infection and 0.01 fatalities. Those numbers are completely possible.

Or what if the 250,000,000 least vulnerable people don't social distance? Then maybe it goes on until herd immunity with 250M infected and 100,000 dead. Perhaps those numbers would have been completely possible, and perhaps the number of dead we're going to see in the USA is going to greatly exceed that.

NYC locked down earlier and locked down more tightly than many other places. And 21,000 are dead out of 8.4 million. If you had the same per capita number of deaths throughout the USA, it'd be over 820,000 dead already.

### US not doing total lockdown

The US is doing a fairly mild lockdown. People are going out to grocery stores and other "essential" stores and encountering people on walks who don't keep six feet away (plus joggers who keep 6 feet but should keep more.) If you have a portion of the population which is not social distancing, which undergoes major infection, it is very difficult for the portion which is keeping social distancing to avoid them. All it takes is one member of your household to have an encounter with them as they attempt to get false herd immunity in their group. It's not how herd immunity works.

If we could find a way that the "liberated" would never, ever interact with those doing social distancing you might make it work. They must never patronize any of the stores we use. They must not work in any of the essential service jobs who have contact with people who are not of their group or the public.

What protects you is that each contact you have in a day has only a minor risk. If it's a normal day where you have hundreds of close contacts with others, that adds to a major risk. If you social distance, you still have smaller but non-zero set of contacts. This increases the risk (not as high as if nobody is distancing but still too high.) It just takes one of your household to get it from them, since you are not distancing from your household.

### Total lockdown isn't possible

What do you mean by "it's not how herd immunity works"?

Yes, the US is doing a fairly mild lockdown. And doing a fairly mild lockdown is the absolute worst thing you can do for this type of virus. You don't contain the virus, plus you shut down the economy.

If you're going to stick with your assertion that "10,000 not social distancing" could be responsible for 250,000,000 being infected, then you should at least define "not social distancing." Is "going out to grocery stores" social distancing? Is "encountering people on walks who don't keep six feet away (plus joggers who keep 6 feet but should keep more)" social distancing? Is working in an essential service job social distancing?

Whatever your definition, I don't see how your numbers make any sense. If 250,000,000 are infected, surely the number of people who are responsible is much much much greater than 10,000.

If we could find a way that the "liberated" would never, ever interact with those doing social distancing you might make it work.

Not "never, ever." For a month or two. If everyone who didn't want to deal with these lockdowns (which will last at least a year or two if they're going to be effective) had thrown a big coronavirus party and all gotten infected, they'd all be immune or dead, or at least hospitalized, by now. And assuming that they were all young and healthy, the number dead would probably be less than the number dead under this "fairly mild lockdown." (The antibody tests are showing this. The mortality rate is much less than we initially thought, and the contagiousness is much higher than we initially thought. If we knew then what we know now, we probably wouldn't have done the "fairly mild lockdown" that we did. Certainly not in NYC, where they ruined the city financially and still had 25% of people infected. 25% and growing. It may very well be 50-80% by a year from now.)

They must never patronize any of the stores we use. They must not work in any of the essential service jobs who have contact with people who are not of their group or the public.

I think you've got it backwards there. If you're too afraid of the coronavirus to go out in public, then you can order all your food to be delivered and you can refuse to go in to work. I do know some people who are doing this. There are some people who haven't been out of their house in months. That's their right. What's not their right to tell me that I can't go to the store.

It's not even in their best interest. The sooner we reach an acceptable level of herd immunity, the sooner they can leave their house.

Moreover, now that we have antibody tests, we can open up stores where all the workers have tested positive for antibodies. The more people who are infected and then recover, the more people who can work in these stores.

### Not backward

I am a free person. So are you, but you are not free to infect me, or take unreasonable risks that lead to my infection. If you have decided to take those risks, so be it, but now it is you who must get out of my way, not I who must stay inside to cower in fear of you. I mean it's probably smart of me to cower in fear of you, but it's your fault that you are dangerous, not mine.

If a group of people want to self-infect to get it over with, they can, but only if they take the duty of staying away from people who are trying to avoid the infection. The two societies must stay distinct, and all the burden of that goes on the ones breeding the virus within their community.

If you decide to put a biohazard lab on my street, you have the sole duty for proper containment. If you are leaking virus onto the street in front of your lab, you have no right to tell me it's my problem if I want to walk down that street. The duty to not spread the virus you are breeding is entirely and solely yours.

### Yes, I am a free person. Or at least I should be.

I am a free person. So are you, but you are not free to infect me, or take unreasonable risks that lead to my infection.

Life consists of risks. Getting the coronavirus is far from the greatest of them. It's more likely for a healthy person to die from a car crash than from the coronavirus. I agree that I am not free to take unreasonable risks that are the proximate cause of your infection. But going to work is not an unreasonable risk. Going to the grocery store is not an unreasonable risk. These are both reasonable risks. And if we both decide to go to the grocery store, with neither of us having any particular reason to suspect that we are infected, you are as much responsible as I am if that causes you to become infected.

If going to the grocery store is an unreasonable risk, then you shouldn't do it.

If you have decided to take those risks, so be it, but now it is you who must get out of my way, not I who must stay inside to cower in fear of you.

First of all, aren't you staying inside to cower in fear already? The whole point of this is that you are trying to force everyone to stay inside and cower in fear, isn't it?

Secondly, why do I have to get out of your way? Because I have taken an "unreasonable risk"? Please define what risks you deem to be unreasonable, and why.

Are "essential workers" allowed to take unreasonable risks? Are they allowed to go grocery shopping? What happens if you get the virus from them? How do I know that you haven't?

I agree that if I know or have strong reason to suspect that I am sick, I shouldn't be going into the supermarket. But if I don't, then I see no reason why I can't go into a grocery store with the grocery store owner's permission. It is, after all, the grocery store owner that owns the store, not you.

You seem to be much much more fearful of this virus than the vast majority of the population. That's fine. Maybe you have good reasons for it, or maybe you're just being irrational about it. Either way, you are in a small minority, and the majority of the world should not adapt itself to you. If you have some sort of preexisting condition that is beyond your control, maybe you can get some sort of disability. You seem to be able to work from home though, so why can't you just get delivery for your groceries? If it were up to me and you had to do this because of some preexisting condition, I'd support the extra costs being covered by health insurance. But it doesn't cost all that much, and you seem to have a lot more money than most people anyway.

But asking the whole world to shut down because of your preexisting condition isn't reasonable, regardless of whether or not that preexisting condition is beyond your control. We don't build a bubble around the world to protect an immunocompromised individual. We build the bubble around the immunocompromised individual.

If a group of people want to self-infect to get it over with, they can, but only if they take the duty of staying away from people who are trying to avoid the infection.

Do they only have to stay away until they develop antibodies? Unfortunately, I don't think that'd be legal (the stay-at-home orders don't contain exceptions for coronavirus parties or for people who have developed antibodies), but if it were that'd be a much better solution than what we've done, especially if we stopped all the government subsidies to people who don't truly need it. And as I said before, it'd mean we'd have far fewer deaths, because the it's the young and healthy people who will tend to take that deal, and as the number of people with antibodies goes up, the effective R0 goes down.

It still might be a long time before those who are most fearful of this virus are willing to re-enter society (especially if they can work from home or don't mind living in poverty off of government subsidies). As I've said in our other thread, this virus isn't going to be completely eliminated for a very long time. Even with 80% herd immunity, we'll still have outbreaks from time to time.

Eventually maybe there will be a vaccine. The vaccine might not be 100% effective, though, and the vaccine itself will have risks. At some point, you have no choice but to be willing to take some risks.

The two societies must stay distinct, and all the burden of that goes on the ones breeding the virus within their community.

I agree in the case where people are intentionally infecting themselves. But I don't agree that all of the burden goes on me and not you just because you have a job which you can do from home and I don't.

If you decide to put a biohazard lab on my street, you have the sole duty for proper containment.

I didn't put a biohazard lab on your street. I went to work.

### Is going to work an unreasonable risk?

Is can be. Core purpose of lockdown measures is to prevent exponential explosion of the virus in the community. No single person's actions are "too much risk" which is why people understandably chafe at restrictions. However, the sum of a sufficient number of people engaging in the action can generate enough risk to make the explosion upward exponential. Every pattern of behaviour tweaks the base of the growth formula. The goal is to make it less than one. If it's less than one we get exponential decay, and if more than one exponential growth.

So, while they have not the time and data to model it precisely, it will turn out that there is some percentage of the population who could go to work and take other infection risks and keep the R0 below one. The lower R0 the faster the disease dies out.

Let's say that percentage is 50% -- that we can tolerate half the people living ordinary economic lives, but we can't tolerate 100%. At 100% it goes crazy exponential, like we saw in Italy pre-lockdown.

So what do you do? When you have a state, it will pick which 50% (though ideally much less than 50%) get to work, and which don't. The decision taken was to declare some tasks "essential" (like food distribution) and other tasks more and less risky. Work from home is of course low risk. Hair salons and cinemas and churches are high risk.

But everybody wants to be the one given the exception. That makes it hard. What's confusing about my writing is that when I say, "If you decide to join a group of people who are not limiting spread of the virus, then you are putting me at risk." It's true, but because the particular risk from you to me is small, it's hard to understand. The risk is that there are groups of people deciding to be virus breeding pools.

But how do you prevent the groups? Right now, only by preventing the individuals.

It is made harder by the fact that we don't know what the numbers are. I used 50% above as an example number for illustration. Without data on what the number really is, on what the risk of the different activities really is, you have to err on the strict side. If you are too loose, you get exponential growth and death for which there is no undo. If you are too strict, it's hard, but there is an undo.

In my artice, I outline how, if you get a modest sized group who decide to be virus breeders, and they trigger the exponential explosion, their liability for the damage they do to everybody else is so great that they would be wise to stay inside. The reason is the way exponential math works. As the group size grows linearly, their damage grows exponentially, and each member's share of the damage becomes untenable. This is true even though you don't see the issue with just being a member of the breeders and walking past me, or shopping in the store I go to.

You suggested that if I want to fear the virus, I should stay home. But the protest groups are putting a biohazard lab on my street, with no containment effort at all -- in fact they are publicly and proudly declaring their lack of desire to contain it.

### Yes, no, okay

You suggested that if I want to fear the virus, I should stay home.

Yep.

But the protest groups are putting a biohazard lab on my street, with no containment effort at all

No, they aren’t. They’re engaging in their constitutional right to protest.

Let's say that percentage is 50% -- that we can tolerate half the people living ordinary economic lives, but we can't tolerate 100%.

Sounds good. Now rerun your numbers with 150,000 people causing 250,000 infections.