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

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

The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2019.12.19.882175 doi: bioRxiv preprint these differences and are they biologically meaningful or spatially random?" 221 A cursory review of the recent literature suggests that the gravity model is the most 222 prominent in the infectious disease context, followed by the radiation model. Stouffer's 223 model and the competing destinations model have rarely been applied in this field. It is 224 therefore useful to use the gravity model fit as a baseline and explore how the 225 better-fitting models diverge from this baseline. Comparing matrices with half a million 226 entries is very difficult, so we amploy a new 'spatial likelihood contrast' (SLiC) method 227 with which to study the relative merit of the different spatial interaction models. The 228 idea is to disaggregate the overall hazard likelihoods by individual cities to study how 229 particular communities contribute to improved or diminished relative fit of each model. 230 To do so we normalize each location's contribution to the overall likelihood by the 231 number of data points each conurbation contributes to the likelihood (the accumulated 232 stretches of measles absence) and then map the model-model differences onto the 233 landscape (Fig. 3) . Inspection of Fig. 3 suggests that the poorer fit of the gravity model 234 vs. the Stouffer or competing destinations models is primarily in the urban northwest. 235 The supplement provides the full set of pairwise SLiC contrasts among all models. To 236 test whether the apparent patterns are statistically significant, we compute local 237 indicators of spatial association (LISA; [34] ) statistics for all population centers with 238 fewer than 50k inhabitants (Fig. 3A, B) . The main failure of the gravity model is in (e.g. [35, 36] ). In the case of epidemics playing out within a population center, models 254 closer to the mean field model (i.e., with uniform connectivity) often do remarkably well 255 (see [37] for a social network perspective on this). However, such models generally do 256 not capture regional spread of human infections because of the complicated patterns of 257 human movement (the third wave of the 2009 influenza pandemic across the USA, 258 perhaps, being an unusually diffusive counterexample [7] ) . To elucidate these patterns, 259 many empirical studies have been performed and a variety of abstractions have been 260 proposed. The task of choosing among these abstractions for help in help predicting 261 spread of infectious disease is complicated by the fact that (i) model formulations may 262 differ with respect to how well they actually reproduce aggregate mobility patterns, and 263 (ii) model fit may be shaped by the manner in which mobility is filtered by transmission 264 and behavior.