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

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

Several spatial interaction models have been parameterized and tested using various 61 mobility data such as commuter flows (e.g., [5, 14] ), mobile phone geolocations 62 (e.g., [16] ), social media (e.g., [13] ), and microsimulations (e.g., [17] ). However, in view 63 of the challenges just noted, the ultimate test of the models is against data on the actual 64 spread of infection rather than bulk movement of people or cell phones. Bjørnstad and 65 Grenfell [18] proposed that for acute immunizing infections, the spatio-temporal 66 patterns of fade-outs (i.e., local disease extinction) across metapopulations provide 67 valuable information on disease spread because these patterns reflect spatial 68 transmission unclouded by local transmission. In this paper, we extract information 69 from fade-out patterns and a consistent likelihood framework to compare and contrast 70 to a suite of models including (i) the gravity model [1] , (ii) Fotheringham's competing 71 destinations model [10] , (iii) Stouffer's rank model [12] , and (iv) the radiation model [14] . 72 . We confront these models weekly data on measles incidence from all 954 cities and 73 towns in England and Wales from 1944 to 1965 [4, 19] . Comparing fits and predictions, 74 we show that while the gravity model is a reasonable first approximation, Stouffer's 75 rank model, an extended version of the radiation model, and the competing destinations 76 model all provide significantly better fits, Stouffer's model performing the best.