Related to: Forty Days , Low Hanging Poop
From professor Gregory Cochran's blog West Hunters.
Laurie Garret has an article out in the Washington Post. She say that there’s no point in trying to block the spread of Ebola by travel bans.
The problem is, she’s full of crap. Look, there are two possible scenarios. In both of them, r, the number of new cases generated by each case, is greater than 1 in parts of West Africa – which is why you get exponential growth, why you have an epidemic. If r < 1.0, the series converges – a case generates a few extra cases before dying out.
Everything we know so far suggests that even though it is greater than 1.0, r in West Africa is not all that big (maybe around 2), mostly because of unfortunate local burial customs and incompetent medical personnel.
It seems highly likely that r in US conditions is well under 1.0 which means you can’t get an epidemic. However, r is probably not zero. It doesn’t mean that you can’t get a few cases per imported case, from immediate contact and hospital mistakes. As an example, suppose that on average each case imported to the US generated a total of two other cases before dying out (counting secondary, tertiary, etc infections). Then, on average, the number of US citizens infected would be twice the number of infected visitors.
Now suppose that a travel ban blocked 80% of sick people trying to fly here from Liberia. We’d have 80% fewer cases in US citizens: and that would be a good thing. Really it would. Does Laurie Garret understand this? Obviously not. She is a senior fellow for global health at the Council on Foreign Relations, but she is incompetent. Totally useless, like virtually everyone else in public life.
We hear people from the CDC saying that any travel restrictions would backfire, but that’s nonsense too. One might wonder why they say such goofy things: I would guess that a major reason is that they were taught in school that quarantines are useless (and worse yet, old-fashioned), just as many biologists were taught that parasites are really harmless – have to be, because evolution!
In the other scenario, r > 1.0 in US conditions as well, or at least is greater than 1.0 in some subsets of the US population. This is very unlikely- even more unlikely considering we can adjust our behavior to make transmission less likely. But suppose it so, for the sake of argument. Then you would want – need – to stop all travelers from the risky regions, because even one infected guy would pose a huge risk. Some say that blocking that spread would be impossible. They’re wrong: it is possible*, although it wouldn’t happen, because we’re too crazy. In fact, in that scenario, we’d be justified in shooting down every plane that _might_ carry an infected passenger. This scenario is the one that fits Garrett’s remarks, but if she really believed it, she would be frantically buying canned goods and finding a cave in the Rockies to hide her family in.
*the Atlantic is pretty wide.
Some people here, including the founder, believe that recursive AI self-improvement is a realistic possibility, but I'm pretty sure that even the most hardcore believers acknowledge that there are physical limits, and that you can't just expect an exponential function to be a good fit for a trend when you get close to the limit.
The basic function you should be looking for modelling this kind of phenomena is the logistic function. It's the basic model for phenomena that include both positive feedback mechanisms (e.g. self-replication) and negative feedback mechanisms (e.g. resource constraints).
If you look at the graph of the logistic function, you may notice that initially, when positive feedback is dominant, it very closely resembles an exponential, then it becomes about linear around the middle point and then, negative feedback is dominant, it becomes close to a negative exponential.
If a disease had a constant basic reproduction number , and it could infect anyone, and infected people never died because of the infection and remained infectious for life, then the prevalence of the disease over time would be well approximated by a logistic function, with the world population size as the supremum value (the "capacity").
In an actual epidemic, of course, people can die or heal, and the R factor varies over time as the disease spreads to different places, people and institution change their behavior, better treatment becomes available, and so on, thus you don't really get an exact logistic trend, but that's the first-order model for forecasting the long-term prevalence disease, not an exponential model that neglects feedback loops.
An exponential model is only useful when the disease prevalence is still quite far from the capacity, that is, when a typical infected person is mostly surrounded by uninfected (and infectable) people.
So, do you think that half of the population will be infected?