Mathematical models of human mobility of relevance to malaria transmission in Africa

May 16, 2018

Abstract: 

As Africa-wide malaria prevalence declines, an understanding of human movement patterns is essential to inform how best to target interventions. We fitted movement models to trip data from surveys conducted at 3–5 sites throughout each of Mali, Burkina Faso, Zambia and Tanzania. Two models were compared in terms of their ability to predict the observed movement patterns – a gravity model, in which movement rates between pairs of locations increase with population size and decrease with distance, and a radiation model, in which travelers are cumulatively “absorbed” as they move outwards from their origin of travel. The gravity model provided a better fit to the data overall and for travel to large populations, while the radiation model provided a better fit for nearby populations.

Methods

Our surveys did not collect information on individuals who had not traveled in the last year, and so to determine whether origin population size had a significant influence on movement frequency, we used equivalent data from national Demographic and Health Surveys (DHS) for each of the survey countries. Geocoded responses to question V167, which measured the number of overnight trips taken by respondents in the last year, were linked to communes/wards having the nearest centroid and used to calculate the proportion of male and female respondents who didn’t travel and the mean number of trips taken by male and female respondents, with weightings to account for differences in demographic sampling rates. These summary statistics were then plotted against origin population size for each survey country. Interestingly, there was no suggestion of a relationship between origin population size and travel frequency for either males or female respondents (Supplementary Figure 1), allowing us to explore the application of gravity and radiation models conditional upon the location of origin.

Fig. 1

Empirical and model-predicted travel frequencies for each survey country. Model predictions are for the gravity model with the destination population size raised to a power, τ, and radiation model B fitted to data for each country individually. Each dot represents a commune or ward, the radius of which is a monotonically increasing function of its population size. Each line represents travel frequency between communes/wards, the width of which is proportional to travel frequency.

Discussion

We fitted human movement models to trip data from a survey conducted in Mali, Burkina Faso, Zambia and Tanzania10. Two benefits of these data were that: (i) only overnight trips were recorded – i.e. trips of relevance to malaria transmission – and (ii) demographic and trip details were recorded, allowing trips to be categorized according to traveler group – namely, women traveling with children in all survey countries and youth workers in Mali. Two models were compared in terms of their ability to predict the observed movement patterns: (i) a gravity model, in which movement rates between pairs of locations increase with population size and decrease with the distance14, and (ii) a radiation model, in which travelers are cumulatively “absorbed” as they move outwards from their origin of travel15. The gravity model provided the best fit to the data overall, as measured by the likelihood of the data under each model; however, neither model was uniformly superior in its predictive ability. In general, the gravity model provided a better fit for travel to large populations, while the radiation model provided a better fit for nearby populations. Significantly different model parameters were obtained for two traveler groups compared to the population as a whole, with youth workers being more attracted to large population centers, and women traveling with children being less attracted