Several indices representing a set of different movement aspects are used for this analysis and described below and then used to infer relative risk of importation.
The aim of this index is to represent travel from core affected countries to other countries related to the long term migration patterns from these countries. We assume that travel between countries increases if there is a history of migration between these two countries (for example to visit relatives). For this purpose we use an existing migration dataset to develop this metric. We estimate the relative number of travellers moving from each of the core Ebola-affected countries to each other country as the estimated total migration between the two countries (in either direction) between 2005 and 2010 using estimates provided by Abel & Sander (2014). I.e. the sum of the estimated number of people who were living in country A in 2005 and were then living in country B in 2010 and the number of people living in country B in 2005 and then country A in 2010. In order to remove estimates of 0 travellers (which would lead to 0 estimates of relative risk, which could incorrectly be interpreted as 0 risk), we added 1 to all of these numbers to represent low but non-zero international travel. Country names were manually matched between those presented by Abel & Sander and those used in the INFORM database.
The aim of this metric is to represent regional and global travel. As there is scant publicly available data on the numbers of people moving between countries, we instead apply a simple parametric model, the gravity model, to infer relative movement based on population sizes and distances. The model takes the form: $\frac{PQ}{D\gamma}$ where $P$ and $Q$ are the populations of the origin and destination countries and $D$ is the distance between geographic centroids of these two countries. $\gamma$ is a parameter controlling how the number of visitors decays with distance. Note that we omit the additional parameters present in other implementations of the gravity model as the later rescaling of the index removes their effect. In the absence of a reliable, publicly available global dataset on international short term travel, the choice of the parameter $\gamma$ becomes arbitrary. We set $\gamma$=1.5 to produce movement rankings that correspond to a prior belief that travel to populous countries in the West Africa region (e.g. Ghana and Nigeria) will be more common than travel to the very populous countries in Asia (e.g. China and India).
This metric aims to represent relatively small-scale cross-border travel in the West Africa region. We initially calculate the number of borders an individual would need to cross to move between two countries (for adjacent countries this number is 1, nor non-adjacent countries which share a common neighbour this is 2, etc.). To produce an index positively related to risk, we converted these codes into an index of adjacency with a score of three for immediate neighbours, 2 for those countries separated by one other country, 1 for those separated by two other countries and 0 for those separated by three or more other countries.
For each of these three indices, we weight connectivity to each of the three core affected countries by an estimate of the prevalence of Ebola in each of those countries to produce a single value of the index for all other countries. For each of the three core Ebola-affected countries, we estimate the current prevalence of Ebola cases by dividing the number of cases reported in each country the last 21 days by each country’s population. By multiplying this country-specific prevalence by the relevant index of movement, we produce an estimate of the relative rate of importation from each of the core countries to each of the other countries. For each country we sum the estimated relative rate of importation from each of the three core countries to calculate an estimate of the overall relative rate of importation into the unaffected countries. These numbers are then rescaled so that the country with the highest importation risk has a score of 10 for the given index and all other countries have a score between 0 and 10 representing the risk relative to the most at-risk country.
In order to incorporate expert knowledge about the relative importance of different modes of movement - as well as on the reliability of each of the different indices - weightings may be provided for calculating the overall Importation Risk metric.
Note that due to a lack of data, this estimation necessarily makes a number of assumptions, and does not represent the expected number of importations over a given time frame. Key points include:
Abel GJ & Sander N (2014) Quantifying Global International Migration Flows. Science 343 (6178), 1520-1522 http://dx.doi.org/10.1126/science.1248676