### Why H1N1 spread so fast

I heard a talk last week at the Intelligence and Security Informatics Conference (ISI2009) about the models used for disease spread, and I realized why the WHO (and everyone else) were surprised by the speed with which the H1N1 flu spread. These models have different assumptions about the probability of spread from one person to another, how much time each individual is infectious, ill, recovering, and immune or not. But they tend to have one underlying assumption about spread, and that is that it’s a planar phenomenon. Spread is usually modelled as a differential equation, a kind of model that if 500 people are in a school and the probability of infection is 10% in a day, then 50 people will become infected.

The problem with these models is that they don’t take into account the “six degrees of separation” phenomenon. Although most people mix with only a small number of people who are geographically close, enough others mix with people who are geographically far away. As a result, after 3 transmissions, the infection hasn’t reached half the world’s population — but it has reached half way around the world!! Failing to take into account the connectivity between people makes the models far, far too conservative about spread.

Including the graph structure that connects people shows that quarantine mechanisms cannot possibly work. These long-distance connections apply at all scales, not just between countries. So if there’s an outbreak in a single city block, there will be some people who have travelled a few miles away before the infection is detected; in an outbreak in a city, there will be some people who have been to another city; and so on.

Of course, the work on “six degrees of separation” was based on communication, which does not always imply transmission. So the constants might be a but larger; but it seems clear that the pass-the-parcel (pass-the-virus) graph can’t have much larger diameter.