Sunday, October 25, 2009

Why is h1n1 a big deal? (and why you should get the vaccine if you can)

First off, I need to get this out of the way
Bill Maher is an idiot.

I think it's appropriate for anyone writing about H1N1 and vaccines right now to also begin their post with that comment.

With that out of the way, it seems there is a lot of confusion out there about what make H1N1 special this year. Depending on where you read it seems that it is either more infectious, just as infectious, or less infectious than the regular flu. Same goes for the intensity of the infection. Adults in their 20s and 30s may be most susceptible, or it may be the regular group of immune deficient, elderly, children and pregnant who have the most to worry.

I can't answer any of these questions for you. But I can show you why you should care about this influenza virus, and if at all possible why you should get the vaccine (if you are in Canada you definitely can get the vaccine; there was enough preparation to make sure that there is enough vaccine for everyone).

The key difference about H1N1 is that virtually nobody is immune to it. With the regular seasonal flu mutation is small enough that year over year there is some immunity that carries over, and this is enough to get a herd immunity effect. I think that this is one of those points that seems so obvious to epidemiologists and infectious disease specialists that they forget to mention it most of the time. But the one time I did hear it mentioned I was reminded of a very simple epidemic model I had constructed a few years ago.

The model attempts to mimic the behavior of a 100 person clique (100 people who are all equally connected to each other) after an infected patient 0 is introduced to the group. I assume that for every day a person is infected they have a 0.3% chance of infecting any other person in the clique; that is there is a 3/10ths of a percent chance that the infected individual will interact with someone else and that interaction results in a transmission of the infection. And I assume that an individual is infectious for 3 days.

Disclaimer: There is no reason to believe any of these assumptions estimate anything about reality. In fact most social networks aren't made up of cliques of this size - you actually have some people who are more connected and some who are less. And there's no reason to believe that your butcher goes to the same banker that you go to (which is necessary for a clique). Plus the 0.3% and 3 days numbers are completely made up numbers. This model has no predictive power.

However, I'm not trying to make a prediction of the intensity of an epidemic; I'm simply want to show some of the characteristics or rules of an epidemic. To make a somewhat opaque metaphor, I wish to show the shape, not the size, of an epidemic. Specifically I want to show that (a) herd immunity is real and (b) once an outbreak begins it is hard to stop.

To see this let's look at the cumulative distribution given for various numbers of vaccinations. These show the probability of how many people will get infected before the infection burns out (that is until no-one is left infected). These values were generated with fortran 95 code using 500,000 trials per vaccination level (pro tip: learning fortran is a stupid way to spend an afternoon).

What this cumulative distribution shows is the probability that an outbreak can be bounded by a particular size. So the chances that less than 45 people will be infected when 20 have been vaccinated is about 60%.

Notice that in the cumulative distribution, the more people vaccinated (or those who come in immune) the higher the graph starts on the left. This shows that the more people you vaccinate the higher the chance that patient 0 won't be able to infect anybody else. This is kind of obvious when you think about it. The more immune people out there the more likely the people patient 0 interacts with are immune. So if nobody is immune there is only a 14% chance of no further infection. But if you immunize 20 people that number jumps to 21% (again, these numbers aren't at all predictive as to the size of the effect).

Also notice the more people you immunize the quicker you get to 1 in the cumulative graph. This is herd immunity fully kicking in. So if no-one is immunized herd immunity will almost certainly mean no more than 90 people will get infected. But if you immunize 40 people it knocks down the maximum size of the epidemic to about 40 people.

Also note the flat line in the middle of the 0 vaccinated cumulative plot. What this shows is that once 8 or 9 people get infected it is very unlikely for the infection to burn out until it reaches at least 60 people. The more people who are vaccinated this line is shorter and more steep. This means that the more people who get vaccinated, the less capable an outbreak is of sustaining itself.

All this to say that introducing a new flu, where very few people are immune, has a big effect on the number of people infected. The less people who are immune the more likely an outbreak is to happen and the larger that outbreak is expected to be.

In the next post I will examine how much getting vaccinated assists those who don't get vaccinated.


Anonymous said...

The less people who are immune the more likely an outbreak is to happen and the larger that outbreak is expected to be.

There are a couple of assumptions that a lot of people are making:
1. That because a virus is new, fewer people are immune
2. That because people lack immunity, it is more likely to spread through the population.

Although you realize and stated that your epidemiological model doesn't represent reality, many people think that the scenario you presented accurately depicts how influenza actually spreads. In reality, H1N1 doesn't appear to spread this way at all. Some people seem to get it out of the blue, while others get it along with dozens of others in close proximity. This seems to suggest that there is either an existing immunity, or very selective transmission. Either way it's difficult to accurately predict the spread.

steven said...

Excuse me for being a little defensive but I really think there are some serious problems with your comment.

I don't think 1 is an unreasonable assumption. And to be fair, I'm not assuming 2; I've constructed a model that supports point 2. A very simple model with acknowledged flaws. But I think it's a pretty shady rhetorical device to call a model result an assumption.

People also used to think that the only reason why some were spared when Noro went through a closed community. Turns out herd immunity was a simpler explanation.

To be frank, I am very skeptical of any theory whose evidence is that there appears to be too much clustering. We see time and time again that people are very bad at recognizing what level of clustering is just an artifact of chance. There are tools to show over clustering and I think it's necessary to go through at least some attempt at rigor when using it as an argument. There's just been too much woo science that has come out of people who think they see patterns in clusters.

James said...

Fantastic job on taking the noro problem and applying it to h1n1. I'm truly impressed.

One thought: You assumed that there is a 0.3% chance of infecting any other person. If we further assume that applying a frequent hand-washing regemin throughout the population pushes the chance down to, say 0.2%, what then happens to the curves?

Can then anything be said about hand washing be more or less important than immunization?


steven said...
This comment has been removed by the author.
steven said...

Thanks Jimmy. Yeah, this is pretty much just the preliminary model from back in the day.

I think reducing the infection rate just moves the cdf up and to the left; so pretty much the same effect as immunization though the shape might be a bit different.

I don't really know about which is more effective, but both should certainly increase the herd immunity effects.