Article explained:

Periodicity, synchronization and persistence in pre-vaccination measles
Ramona Marguta and Andrea Parisi
J. R. Soc. Interface, 13, 20160258 (2016) doi: 10.1098/rsif.2016.0258 [Abstract]

Abstract:

We investigate the relationship between periodicity, synchronization and persistence of measles through simulations of geographical spread on the British Isles. We show that the establishment of areas of biennial periodicity depends on the interplay between human mobility and local population size and that locations undergoing biennial cycles tend to be, on average, synchronized in-phase. We show however that occurrences of opposition of phase are actually quite common and correspond to stable dynamics. We also show that persistence is strictly related to circulation of the disease in the highly populated area of London and that this insures survival of the disease even when human mobility drops to extremely low levels.