Saturday, March 21, 2020

epidemics and human contact statistics...

way back when, my colleague Eiko Yoneki built the Fluphone project, which has suddenly become rather relevant again after a decade. Some folks in Singapore have nicely done something similar with good privacy properties! NHSx are on it in the UK, as are lots of other people...

we had earlier studied human contacts - here's a paper by Augustin Chaintreau et al based on work in the Haggle project which involved empirical studied of how the time between and duration of encounters between people is distributed.  Some of the data sets are freely available in the excellent Crawdad repository.

When modeling an epidemic (e.g. to figure out whether it will collapse, sustain, or go pandemic), people start with the SIR model (susceptibility, infectiousness and recovery) - this basically leads to classic S curves over time for the number of people infected (or fraction of the population) - the other important number quotes is R0 - the number of people each infected person passes the disease on to. Recovered people usually have some level of immunity, so they are "removed" from the population, and not typically returned to the pool of susceptible people (at least for some time, depending on disease and person).

Some problems with naive models:
the values for S,I,R are population averages. As is R0. In fact, R0 obviously varies over time, as the number of susceptible people an infected person can meet must typically decrease.

In fact susceptibility for a disease also can be influenced by prior incurred immunity. This can vary with age, gender and other factors, inherently, or because of similar prior infections, or because of vaccination.

As can infectiousness (simple example - if you are asymptomatic carrier of a disease spread only by coughing, then if you don't cough, it is hard to spread it.).

The point of the encounter data above is that that also isn't simple. People have varying levels of popularity ("degree") and centrality (they are on the path between more or less friends (of friends (of friends (of friends)))) to the sixth degree and more. One study of this by Watts et al shows how this leads to multi-scale, resurgent outbreaks. Ground truth needs us to test everyone!

Vaccination programs often target the vulnerable groups (seasonal flu), but sometimes target the whole population, but possibly indirectly - e.g. if you vaccinate enough kids against measles, mumps, chickenpox, polio, smallpox, and it lasts til later life, eventually there's almost no-one in the population left to spread the thing anymore. The vaccine can be made from a weakened version of the disease, which then "teaches" the human immune system in a way that lets it respond appropriately to the full-strength one later. Herd immunity normally refers to having enough of the population vaccinated that the SIR model tells you the disease won't get anywhere far before only meeting immune people.

The contact interval/duration models are power law and clustered. This tells us that they are driven by heavy tailed distributions of popularity (aka rich get richer, in trading terms), but also affinity (e.g. kinship, friendship, work relationships, etc).  For social distancing to work, you need to combine breaking all these kinds of links, social, work, entertainment, even (actually, especially family if you have a tight knit generational spread!). but also you need to target high popularity or high centrality people especially - this has been used by people in a wide range of areas such as offering advice on safe sex to sex workers to reduce HIV spreading, and even smoking and obesity (e.g. see Christakis work there).

The point of this blog (which may contain errors-  please send me corrections if you spot any!) is to try to explain that it is relatively complex to deal with real outbreaks. When we have phase changes in epidemics, and power law coefficients, some small changes can really fix things, other changes have to be very significant to make a difference. We need adaptive, and (as seen here on heterogeneous) responses. Above all, we need continuous, and continuously more accurate, measurement of all of the above to do this adaptation precisely.

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