First author

Generally, host density is thought to control the spread of infectious diseases — transmission cannot be sustained below a certain density or 'abundance threshold'. Stephen Davis, a postdoc at the University of Utrecht in the Netherlands, and his colleagues combined archived records of plague-carrying great gerbils (Rhombomys opimus) in Kazakhstan with satellite imagery of gerbil burrows. They applied percolation theory — typically used to model liquid flows in porous media — to show that both the distance and amount of contact between hosts can also predict disease outbreaks (see page 634). Davis suggests that percolation theory might provide an alternative framework for disease transmission, especially in wildlife.

Where did you start?

Plague-monitoring programmes were put in place in Kazakhstan in the 1940s, and ran until shortly after the 1991 collapse of the Soviet Union, when they could no longer be sustained. The European Union then helped to salvage and digitize these remarkable data. Abundance thresholds are frequently used by theorists, but our previous analysis of the data showed that plague in gerbils is a rare empirical example of such a threshold that reliably predicts outbreaks of disease. I wanted to know what biological mechanisms created the abundance threshold.

When did you realize percolation theory might work?

I initially applied the usual assumptions about host contacts being random, but it was like pushing a square block into a circular hole. Co-author Pieter Trapman introduced me to percolation theory and co-author Herwig Leirs asked if I had seen Google Earth. This allowed us to identify vast gerbil burrow systems in Kazakhstan. We then had data on three spatial scales — the distances fleas and gerbils move, disease monitoring over a long time period, and the burrow landscape — which is rare. Once we had put all of these data into a model, we found that a percolation threshold — an estimate of disease spread based on long-range connectivity of gerbil populations — emerged immediately.

Will percolation theory supercede the traditional approach?

No, but it's a shift in perspective. It depends on how hosts interact. Humans mix freely, but prey animals such as gerbils can't wander far from their burrows. If you look at host movements in the context of the landscape they inhabit, you can sense whether percolation might be relevant. That it is relevant to plague is surprising, because for a vector-borne disease in a vertebrate host to face such low mobility is unexpected.