A rough and dirty estimate of the COVID externality of visiting your family in the USA for Christmas when you don’t feel ill [EDIT: this calculation low-balls the externality, see below]:
You incur some number of μCOVIDs[*] a week, let’s call it x. Since the incubation time is about 5 days, let’s say that your chance of having COVID is about 5x/7,000,000 when you arrive at the home of your family with n other people. In-house attack rate is about 1⁄3, I estimate based off hazy recollections, so in expectation you infect 5xn/21,000,000 people, which is about xn/4,000,000 people.
How bad is it to infect one family member? Well, people tend to be most infectious about 1.5 days before symptoms show, which is about 3.5 days after they get infected. Furthermore, we empirically see that R is about 1 on average, so the people you infect each infect one person, who goes on to infect one other person, etc. How long until the chain ends? It looks like vaccines will be widely distributed in the USA some time between the 1st of April and the 31st of December 2021. Median date looks kinda like the 1st of September. So let’s say that there’s 8 months of transmission. A month has about 30.5 days, so that’s 244 days of transmission, which is 244⁄3.5=70 people. IFR is about 0.5%, so you get about 70 × 0.5% = 0.35 deaths. Each death loses maybe 13 life-years, altho that’s not quality-adjusted. Since I don’t want to quality-adjust that number, that’s 13 × 0.35 = 4.55 life-years lost. But some infections result in bad disability but not death. I estimate the disability burden at about equal to the mortality burden, so that’s 4.55 × 2 = 9.1 QALYs lost. A year is 365 days, so that’s 9.1 × 365 = 3321.5 QALDs (Quality-Adjusted Life-Days) lost.
So: when you travel to visit family, the rest of the world loses about 33xn/40,000 QALDs, where n is the number of family members and x is how many μCOVIDs you incurred over the last week. If you follow microcovid.org’s advice for healthy people and incur 200 μCOVIDs per week, and your family has 4 other people, that’s about two thirds of a healthy life-day lost by strangers. There are a bunch of estimates in this calculation, so this number might be off by an order of magnitude.
[*] A μCOVID is a one in one million chance of catching COVID-19.
I recently realized, thanks to a FB comment by Paul Christiano, that this is thinking about things in kind of the wrong way. R is approximately 1 because society is tamping down infection rates when infections are high and ‘loosening’ when infections are low. So, by infecting people, you cause some chain of counterfactual infections that perhaps ends when society notices and tamps down infection, but also you cause the rest of society to do less fun interacting in order to tamp down the virus. So the cost of infecting somebody is to cause everybody else to be more conservative. I’m still not quite sure how to think about that cost tho.
Note: this calculation only accounts for you infecting your relatives who then infect others, and not your relatives infecting you and you infecting others. Accounting for this should probably raise the cost by a factor of 2.
A rough and dirty estimate of the COVID externality of visiting your family in the USA for Christmas when you don’t feel ill [EDIT: this calculation low-balls the externality, see below]:
You incur some number of μCOVIDs[*] a week, let’s call it x. Since the incubation time is about 5 days, let’s say that your chance of having COVID is about 5x/7,000,000 when you arrive at the home of your family with n other people. In-house attack rate is about 1⁄3, I estimate based off hazy recollections, so in expectation you infect 5xn/21,000,000 people, which is about xn/4,000,000 people.
How bad is it to infect one family member? Well, people tend to be most infectious about 1.5 days before symptoms show, which is about 3.5 days after they get infected. Furthermore, we empirically see that R is about 1 on average, so the people you infect each infect one person, who goes on to infect one other person, etc. How long until the chain ends? It looks like vaccines will be widely distributed in the USA some time between the 1st of April and the 31st of December 2021. Median date looks kinda like the 1st of September. So let’s say that there’s 8 months of transmission. A month has about 30.5 days, so that’s 244 days of transmission, which is 244⁄3.5=70 people. IFR is about 0.5%, so you get about 70 × 0.5% = 0.35 deaths. Each death loses maybe 13 life-years, altho that’s not quality-adjusted. Since I don’t want to quality-adjust that number, that’s 13 × 0.35 = 4.55 life-years lost. But some infections result in bad disability but not death. I estimate the disability burden at about equal to the mortality burden, so that’s 4.55 × 2 = 9.1 QALYs lost. A year is 365 days, so that’s 9.1 × 365 = 3321.5 QALDs (Quality-Adjusted Life-Days) lost.
So: when you travel to visit family, the rest of the world loses about 33xn/40,000 QALDs, where n is the number of family members and x is how many μCOVIDs you incurred over the last week. If you follow microcovid.org’s advice for healthy people and incur 200 μCOVIDs per week, and your family has 4 other people, that’s about two thirds of a healthy life-day lost by strangers. There are a bunch of estimates in this calculation, so this number might be off by an order of magnitude.
[*] A μCOVID is a one in one million chance of catching COVID-19.
I recently realized, thanks to a FB comment by Paul Christiano, that this is thinking about things in kind of the wrong way. R is approximately 1 because society is tamping down infection rates when infections are high and ‘loosening’ when infections are low. So, by infecting people, you cause some chain of counterfactual infections that perhaps ends when society notices and tamps down infection, but also you cause the rest of society to do less fun interacting in order to tamp down the virus. So the cost of infecting somebody is to cause everybody else to be more conservative. I’m still not quite sure how to think about that cost tho.
Note: this calculation only accounts for you infecting your relatives who then infect others, and not your relatives infecting you and you infecting others. Accounting for this should probably raise the cost by a factor of 2.
Note: this calculation assumes that travelling is not risky at all. Realistically that should be bundled into x.