Comparison of alternative models of human movement and the spread of disease
Predictive models for the spatial spread of infectious diseases has received much attention in recent years as tools for the management of infectious diseas outbreaks. Prominently, various versions of the so-called gravity model, borrowed from transportation theory, have been used. However, the original literature suggests that the model has some potential misspecifications inasmuch as it fails to capture higher-order interactions among population centers. The fields of economics, geography and network sciences holds alternative formulations for the spatial coupling within and among conurbations. These includes Stouffer’s rank model, Fotheringham’s competing destinations model and the radiation model of Simini et al. Since the spread of infectious disease reflects mobility through the filter of age-specific susceptibility and infectivity and since, moreover, disease may alter spatial behavior, it is essential to confront with epidemiological data on spread. To study their relative merit we, accordingly, fit variants of these models to the uniquely detailed dataset of prevaccination measles in the 954 cities and towns of England and Wales over the years 1944–65 and compare them using a consistent likelihood framework. We find that while the gravity model is a reasonable first approximation, both Stouffer’s rank model, an extended version of the radiation model and the Fotheringham competing destinations model provide significantly better fits, Stouffer’s model being the best. Through a new method of spatially disaggregated likelihoods we identify areas of relatively poorer fit, and show that it is indeed in densely-populated conurbations that higher order spatial interactions are most important. Our main conclusion is that it is premature to narrow in on a single class of models for predicting spatial spread of infectious disease. The supplemental materials contain all code for reproducing the results and applying the methods to other data sets.Author summary The ability to predict how infectious disease will spread is of great importance in the face of the numerous emergent and re-emergent pathogens that currently threatening human well-being. We identified a variety of alternative models that predict human mobility as as a function of population distribution across a landscape. These consider some models that account for pair-wise interactions between population centers, as well as some that allow for higher-order interactions. We trained the models using a uniquely rich spatiotemporal data set on pre-vaccination measles in England and wales (1944–65), which comprises more than a million records from 954 cities and towns. Likelihood rankings of the different models reveal strong evidence for higher-order interactions in the form of competition among cities as destinations for travelers and, thus, dilution of spatial transmission. The currently most commonly used so-called ‘gravity’ models were far from the best in capturing spatial disease dynamics.