Home alone

This year’s first lecture also included some house rules, the first of which was “Please don’t come to class if you’re sick.” This apparently contradictory request seems to have caught on, judging by the amount of e-mail from students coming down with, in the middle of, or not quite recovered from swine flu. For my part, though I would love to have everyone in class every day, I’m grateful indeed that people are staying away when they’ve got a communicable disease.

I haven’t kept accurate records, but in the first three weeks there were at least a dozen self-isolators in my class of 110, so one might estimate that 10 percent of undergrads have already had swine flu. What will happen next? I certainly don’t know, but the World Health Organization (WHO) issued a press release late in August that gave some possibilities. WHO said that “there would be a period of further global spread of the virus, and most countries could see swine flu cases double every three to four days for several months until peak transmission is reached.” (This comes from Wikipedia’s version of a widely disseminated news story.)

Since I’m teaching a QR course, the numbers in this story presented an opportunity for a couple of questions in a problem set. “Suppose there are 1,000 people with swine flu today. If the doubling period is four days and peak transmission is reached after two months, how many people will be infected? (This is the optimistic scenario.) Now suppose that the doubling period is three days and peak transmission is reached only after three months, a pessimistic scenario. How many people will be infected?”

Truly interested readers are invited to pause here and work this out for themselves; the uninterested can read right on for the answers.

Two months is 60 days, so in the optimistic case doubling every four days means that there are 15 doublings. If you were ever in COS 109, you will certainly remember that two to the 15th power is greater than 32,000, so the hypothetical 1,000 original cases have become 32 million, roughly one-tenth of the population of the United States. Things are not so good in the pessimistic case, however. Doubling every three days for 90 days is 30 doublings, and two to the 30th power is more than a billion, so our original 1,000 victims have become well over one trillion. Given that the population of the world is less than seven billion, everyone would have gotten flu well before the end of three months. There are several useful quantitative lessons here, including the approximations that link powers of two (like two to the 30th) to powers of 10 (like a billion), and the important fact that no exponential growth can go on forever.

Of course these are simple-minded models, but diseases do spread exponentially (for a while) if they are contagious enough and if people’s behavior encourages the spread. Hence the request to isolate yourself — you’re much less likely to pass it on.

Whether you’re one of the unlucky 32 million or everyone gets it, it’s no fun to be sick when far from home, and even less so if the flu combines with painful complications like strep throat. If you have nearby family or supportive roommates to bring sympathy and food, they can offer comfort, but it’s still a grim time. I got the regular seasonal flu about 10 years ago, presumably from a student, and I thought I would die; indeed for a couple of the worst days, death seemed like a fine option. Every year since, it’s been a flu shot for me at the earliest possible moment, and so far I’ve have managed to avoid getting sick again. I’m old enough to probably have a few swine flu antibodies from a now-forgotten childhood illness. But just in case, please continue to stay home and enjoy your self-isolation as best you can. Once you’re truly well again, come back to class. It will be really good to see you, and who knows — some of the material might be interesting, useful, and maybe even on an exam.

Brian Kernighan GS ’69 is a computer science professor and a Forbes faculty adviser. He can be reached at bwk@cs.princeton.edu.