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

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

Accurately predicting the geographical spread of emerging, re-emerging, and recurrent 14 epidemics in an increasingly globalized world is a matter of international urgency in the 15 wake of outbreaks of emerging pathogens such as severe acute respiratory syndrome 16 (SARS), Middle East respiratory syndrome (MERS), and ebola virus disease (EBVD) as 17 well as re-emerging and resurgent pathogens such as influenza subtype A-H1N1, 18 whooping cough, and measles. In response to this challenge, various 'spatial interaction' 19 models describing human movement as a function of population distribution have been 20 proposed. Some of these borrow from economics and human geography while others 21 adapt models from movement ecology and the physics of reaction and diffusion on 22 heterogenous landscapes. 23 In recent years, the field has seen the widespread adoption of a family of so-called 24 'gravity' models from transportation theory and human geography (see, e.g., [1, 2] ). In 25 its most common form, the gravity model posits that the migration flux between a pair 26 of cities is log-linearly dependent on their respective sizes and on their separating 27 distance. The application of this simple model to disease spread was originally proposed 28 by Murray and Cliff [3] , but over the last decade, many studies have used it to explain 29 historical, or predict future, disease spread in a range of infections including measles [4] , 30 influenza [5] [6] [7] , cholera [8] , and yellow fever [9] . While its application has yielded 31 insights, the geography literature has highlighted a prominent shortcoming of the 32 gravity model. In particular, these models ignore the potential for competitive or 33 synergistic interactions among population centers ( Fig. 1 ; [10, 11] ). Thus, for example, 34 movement between Boston and Washington DC is assumed to be unaffected by the 35 presence of the intervening city of New York. 36 As it happens, there are distinct families of models, arising from economics and 37 geography, that predict human movement patterns while allowing for higher-order 38 interactions among cities. In particular, Stouffer's [12] 'law of intervening opportunities' 39 posits that "the number of persons going a given distance is directly proportional to the 40 number of opportunities at that distance and inversely proportional to the number of 41 intervening opportunities". This idea has given rise to alternative models for human can feed back onto migration. Most obviously, disease symptoms can influence 53 movement behavior, as seen, for example, in the fact that a mild cold may induce 54 minimal changes in movement behavior but severe hemorrhagic fever or acute paralytic 55 disease will typically slow the movement of the infected hosts. These two considerations 56 do not preclude the utility of spatial interaction models in the infectious disease context; 57 they do, however, complicate their use and the importance of understanding 58 transmission relevant migration fluxes, which will be some sort of 'effective average' of 59 movement as filtered through such aforementioned complications.