Source: Calculated from William and Mary COVID-19 dashboard, accessed 5/9/2022

William and Mary updated their COVID-19 dashboard last night. The most recent new infection rate in the student body is about 100 per 100K population per day. Roughly speaking, the uptick that started a few weeks back is not getting any worse. But neither has it disappeared.

**I looked at last weeks numbers and didn’t get a booster shot. I figured I’d wait to see if this weeks numbers resulted in any greater clarity. No such luck.**

So now, push comes to shove on the question of getting a vaccine booster before attending graduation ceremonies, because those are now less than two weeks away. We’re about at the time limit, as it takes some time for antibodies to build after a booster shot.

### To boost or not to boost?

Time for some ~~guesswork~~ calculation.

**First, I want to guess the likelihood that I’m going to be in the same room as somebody who is infectious with COVID-19.** At that stage, that’s not the odds of getting infected. (Being in the same room does not guarantee infection). It’s just a way to start getting a handle on the riskiness of the situation.

For that, I need two figures: How many people are involved, and what fraction of them are likely to have an active COVID-19 infection?

I expect to attend three small indoor graduation ceremonies, with an average of maybe 100 student and 200 family members each. ** Call that a total cumulative crowd of 900 people with whom I’m be sharing an indoor space. **

Currently, Virginia is averaging 27 new cases per 100K population per day. If we stick to our current trend, that’ll be around 50, two weeks from now. Taking the weighted average of that (for the family members) and 100 new cases per 100K (for the students in attendance), I come up with **an expected average of 67 known new cases per 100K population per day.**

**You have to multiply the new-case rate that by two factors** — one to account for cases that are not officially reported, and one to account for the number of days an infected person typically remains in circulation and capable of infecting others. At various times, I’ve guessed estimates for both of those.

At the low end, I’d multiply the current new-case rate by six. That’s a factor of two, to account for cases not counted in the official statistics, and an average of three days walking around in an infectious state (combining both symptomatic cases and asymptomatic cases). But I could easily see a factor of nine, if you figure there are three true cases, now, for every one that gets officially diagnosed and reported.

**So, take either a nine-fold rule or a six-fold rule as a reasonable way to estimate the number of actively infectious individuals in a crowd, based on the current official daily new case rate figures.**

**Now I do a lookup on a chart I worked up a few months ago.** Once you accept either a nine-fold or six-fold multiplier above, the rest is just math. So the chart itself is nothing but a bunch of arithmetic, tabulated.

Without belaboring the assumptions behind the “N-fold rule”, I think **it’s a foregone conclusion that I’m going to end up in the same room as somebody who has an active COVID-19 infection. **

I don’t think that’s a surprise, given that this boils down to hanging out in a crowd of about 1000 people in the middle of a modest new wave of COVID-19 cases.

**How may people would I expect? Maybe four or five actively infectious individuals,** total, in the crowds I’ll be part of two weeks from now. Same assumptions, just slightly different math.

**Now comes the less-quantifiable part. What are the odds of being infected, given that?** Let’s say there’s a roughly 0.5 percent chance (4.5 persons out of 900) that any one seat in that room is occupied by an infected individual. And, in total, I expect to spend about three hours in situations of that type.

**Literally the only quantitative analysis I have to go on is a study of Chinese train passengers from early in the pandemic.** This has the multiple disadvantages of being a) train service, and b) the original Wuhan version of COVID, for which the R-nought (basic infectiousness) is at least five times lower than the current strains (BA.2 and BA.2.112.1).

Whatever. This is the best I’ve got. This is a study of known infected individuals who took a train trip, and the subsequent infection rates of the people seated around them. I infer from the writeup that these passengers were not wearing masks. I’m just going to fuzzy-up the details, and state the following.

On average, for a relatively short exposure, risk in that study was only observed for persons sitting within two rows and two columns of the infected individual. That means 5 x 5 = 25 seats, less the two occupied by myself and my wife, **or 23 strangers sitting within range of me, at each of three one-hour ceremonies. ** If, by contrast, W&M **leaves every-other-seat empty, then that would mean sitting next to roughly 13 strangers.**

Looking at Figure 4 from that study, at the one-hour mark, averaged across all nearby sites, **the risk of infection was 0.14 percent per hour, for all those seats. ** And, luckily for me, that’s by far highest from the person sitting next to you, on the same row, which will be my wife.

But that was for the Wuhan strain. There’s no direct way to translate it, but the R-noughts of the current strains are at least five times greater than that. So, as a rough cut, let me **multiply that baseline infection (attack) rate by five, to yield 0.7 percent per hour risk of infection,** accounting for the far greater infectiousness of BA.2 and BA.2.12.1 relative to strain B.

**Worst case: ** When I grind through the numbers, I estimate that **if we weren’t vaccinated, and if we didn’t wear masks** (the conditions for the Wuhan train study), and W&M does not leave every-other-seat empty, we’d have about **a 1-in-400 chance of contracting COVID-19,** sometime in the course of three one-hour sessions, given the current new case rates in Virginia and within the W&M student body.

Obviously, that’s a rough cut, but some estimate is better than no estimate.

Now you have to factor in the effects of wearing a properly-fitted N95 mask, and of vaccination and booster. But you also have to figure that every meal we eat, over that time period, is going to be in a packed restaurant. And indoor dining is well-established as a relatively high-risk situation for COVID-19 transmission. If I had to guess, on net, I’d guess that our net risk of all that is at least four-fold smaller than the one-in-400 cited above, due mostly to mask use. (Per prior post, impact of vaccination on probability of getting any infection is now quite small, due to decline in circulating antibodies over time).

**Finally, if we only get one booster, we have to figure out whether or not this is the most risky thing we’re likely to do in the next half-year or so.** If so, might as well use up our one allotted additional booster shot now. Or, conversely, figure out whether they’ll allow yet a third booster shot this fall, as we get the expected winter wave of flu-and-COVID.

### Conclusion

When I put all that in the blender and give it a whirl,** the upshot is that my wife and I have made appointments to get our second booster shot this afternoon.** Obviously, YMMV. We’re in our 60’s and overweight.

**Despite the thin veneer of rationality above, really, I think the deciding factor is probably nowhere near as quantitative as the discussion would suggest.** In the end, the less I have to worry about @#$(!@ing COVID-19, the more I can enjoy watching my daughter graduate from college. And for me, that’s well worth getting my last allotted booster shot before we attend those ceremonies.