While trying to build a better mathematical model for recurrent measles epidemics, biomathematics professor Lewi Stone at Tel Aviv University in Israel and his colleagues came up against a major challenge. Sometimes epidemics come every year, sometimes every two years, sometimes every few years; it's hard to predict.

They found this feature difficult to capture in models — even the nonlinear, chaotic models that they'd devised. But the breakthrough came, thanks in part to the fresh perspective of then-graduate student Ronen Olinky. “He decided to look at the problem from a completely different angle,” says Stone.

Instead of trying to make a model that generates an epidemic each year, Stone and co-author Amit Huppert, on Olinky's suggestion, decided to investigate why in some years the epidemic doesn't come.

They looked at one major influencing factor: a population's susceptibility — how many susceptible individuals (those who have never had measles nor been vaccinated) remain after an outbreak (see page 533).

Seasonality is also key — outbreaks occurring later in the disease 'season' affect fewer individuals and leave more susceptible ones behind. Their model is geared to measles, although Stone is now trying to tweak it for seasonal influenza.