Comparison of alternative models of human movement and the spread of disease

Ottar N. Bjørnstad; Bryan T. Grenfell; Cecile Viboud; Aaron A. King

Data 79 Historical incidence of measles in England and Wales has been an influential testbed for 80 models and methods in disease dynamics since Bartlett's [20, 21] seminal work on its 81 recurrent epidemics. We use the spatially resolved weekly measles data across all 954 82 cities and towns of England and Wales from 1944, when notification was made 83 mandatory by the UK Registrar General (OPCS), until 1965, which saw subtle shifts in 84 political boundaries around London. Vaccination was not introduced in the UK until 85 1967, so that these data span a period where measles dynamics were unaffected by mass 86 immunization. The data set is complete except for a region-wide underreporting rate of 87 around 50% [22, 23] . Grenfell et al. [19] give a detailed description of the data; the 88 entire data set has been made available by Lau et al. [24] . 89 An important feature of the system is that, between 29% and 38% of the population 90 (c. 47M during this period) resided in a small number (13-28 depending on exact 91 definition) of communities above a critical community size (CCS) of c. 250-300k. Cities 92 larger than the CCS tend to sustain local chains of transmission. The remaining 60-70% 93 were distributed among the more than 900 communities smaller than the CCS where 94 local extinctions are more or less frequent (depending on population size and degree of 95 isolation) and, consequently, the rate of reintroduction of the pathogen via spatial 96 transmission is an important determinant of measles incidence. In ecological terms, the 97 prevaccination measles system represented an epidemic mainland-island metapopulation 98 (e.g., [25, 26] ). Our analysis exploits this fact, using the timing and spatial pattern and 99 timing of reintroductions to inform the parameters of each of the spatial interaction 100 models.