*Please note: This is an outdated version of this estimate. An updated version with more accurate numbers can be found here.*

I've been expecting a resurgence of swine-origin influenza virus (SOIV) in North America for a while now, and it hasn't happened. The virus is still out there, still infecting a few thousand people per week, but there hasn't been a third large-scale wave of virus transmission. That's different from the 1918 and 1957 pandemics (see here for details). What's different this year?

Of course there are tons of things that are different this year, but I recently got around to doing something I should have done a while ago: Trying to estimate what proportion of Americans are now immune to SOIV. I've seen estimates that around 40% of the population should now be immune. I get roughly the same number (slightly higher, closer to 50%, because those estimates didn't take into account pre-existing immunity to SOIV), but I think there's an important point that might be missed in this: **Most of the immunity might be clustered in the two most susceptible populations (children and the elderly), with up to 3/4 of them being immune.**

There are three ways someone could be immune to SOIV. They could have been exposed to a related virus, some time in the past, and have developed a long-term immunity. They could have been infected with SOIV, somewhere in the first or second wave. Or, of course, they could have been vaccinated.

Numbers for each of those are available. They're more or less approximate; not all the sources break down age groups in exactly the same way, for one thing, and I don't have precise numbers for everything. ^{1} I'll try to flag places where I'm especially guessing, and it's entirely possible that this I've made some obvious, basic mistakes in here, since this has been written in the interstices of cleaning our house for Chinese New Year (a Herculean task) and hosing down the kids to get them ready for the party at YongHui's this evening. If so, let me know and I'll try to correct them.

We need to break immunity down by age, because pre-existing immunity to SOIV was strongly age-dependent. (That's presumably why the virus was strongly biased to infecting younger people this year.) For the demographics of the US I'm using the 2008 census data. All this is summarized in the table below, and my explanations follow.

Age group | Number | Already immune | Infected | Vaccinated | Vaccinated uninfected | Number immune (low) | Number immune (high) | Percent immune (low) | Percent immune (high) |

0-18 years | 82,640,086 | 3,305,603 | 27500000 | 30,576,831 | 20,486,477 | 51,292,080 | 61,382,435 | 62.1% | 74.3% |

19-64 years | 182,549,922 | 10,952,995 | 22000000 25000000 | 38,335,483 | 25,684,774 | 58,637,769 61,637,769 | 71,288,478 74,288,478 | 32.1% 33.7% | 39% 40.7% |

65 and older | 38,869,716 | 13,215,703 | 5500000 2500000 | 11,334,214 | 7,593,923 | 26,309,627 23,309,627 | 30,049,918 27,049,918 | 67.7% 60% | 77.3% 70% |

Totals |
304,059,724 |
27,474,302 |
55000000 |
80,246,530 |
53,765,175 |
136,239,478 |
162,720,833 |
44.8% |
53.5% |

**1. Pre-existing immunity. **A paper in New England Journal of Medicine last year ^{2} found that 4% of children, 6% of young adults, and 34% of older adults (born before 1950; I'm going with 65 years old as the dividing line just to make it easier to compare to other data) were already immune to H1N1. That's more or less consistent with other studies I've seen, so let's go with that.

**2. Infection. ** The CDC estimates that somewhere over 55 million people in the US were infected in the first and second wave of SOIV. I don't have age breakdowns of this, though I think they're out there in some form. Based on the demographics of infection I've seen, I think it's reasonable, if pretty approximate, to guess that half of these infections were in children (under 18), 40% were in young adults, and just 10% were in older adults over about 65. ^{3} **Edit:** *That doesn't look right -- too high a proportion of the elderly infected. I arbitrarily shifted some to the younger adult population and out of the elderly. It doesn't change the conclusions significantly. * This works out to a third of US children being infected with SOIV, and again it's broadly consistent with measures elsewhere -- for example, a recent Lancet paper ^{4} that estimated that about a third of children in the UK were infected.

**3. Vaccination. **The CDC's Anne Schuchat's Feb 5 press conference was very useful for this. The CDC has estimated that somewhere over 70 million people in the US have been vaccinated. Schuchat gave two further figures: Some 37% of children, and about 21% of adults have been vaccinated. These figures come from two different sources -- a CDC survey and a Harvard survey respectively -- so they may not be directly comparable, and I don't know the breakdown in adults (young adults vs. elderly) but these figures do work out to about the right total, around 80 million people. Probably a little high, but not by much.

Another source of fuzziness is how much overlap there is between infected people and vaccinated people. It's probably safe to say that most vaccinated people were not subsequently infected, but it's quite possible that people were infected (perhaps with no symptoms, which we know happened quite frequently) and were subsequently vaccinated. ((This is another significant potential source of error, I think.)) I've tried to adjust for this by assuming that either a third of the vaccinated were already infected ("vaccinated uninfected"; trying to avoid double-counting), or by assuming none were (just plain "Vaccinated"), to get a range of immunity out there.

Including "Vaccinated uninfected" gives the "Number immune (low)"; assuming that all vaccinated were not infected gives the "Number immune (high)".

And my **conclusions **are that:

- Between 45 and 55% of the US population as a whole is now immune to the new SOIV.
- As many as 3/4 of the elderly and children -- the most important populations as far as flu is concerned -- may be immune.
- Between a third and about half of this immunity was due to vaccination.

That level of immunity is probably enough to impact virus transmission drastically. In the early waves, if a child was infected then virtually every child she contacted in school or on the playground would be susceptible. Now only a third or a quarter of them are potentially infectable. I'll have to spend some time looking at the models of influenza spread but I think that considering that the SOIV was not spectacularly infectious anyway, this level of population immunity is easily enough to prevent the third winter wave of disease I was expecting to see.

(I am particularly curious about modelling the impact of vaccination. Without vaccination would there have been a third wave? My guess is that there would have been, but that's just a guess.)

What's more, this level of immunity, especially in the apparent absence of the usual seasonal flu strains, has important implications about influenza over the next few years, but this post is already too long, so maybe I'll talk about that some other time.

1. Probably quite accurate numbers are available, but not to me. Or, at least, not without a lot more work.

2. Hancock, K., Veguilla, V., Lu, X., Zhong, W., Butler, E., Sun, H., Liu, F., Dong, L., DeVos, J., Gargiullo, P., Brammer, T., Cox, N., Tumpey, T., & Katz, J. (2009). Cross-Reactive Antibody Responses to the 2009 Pandemic H1N1 Influenza Virus New England Journal of Medicine, 361 (20), 1945-1952 DOI: 10.1056/NEJMoa0906453

3. This is at best an educated guess, and may be the most fuzzy number in this back-of-the-envelope calculation here.

4. Miller, E., Hoschler, K., Hardelid, P., Stanford, E., Andrews, N., & Zambon, M. (2010). Incidence of 2009 pandemic influenza A H1N1 infection in England: a cross-sectional serological study The Lancet DOI: 10.1016/S0140-6736(09)62126-7