EpiRisk
EpiRisk is a computational platform designed to allow a quick estimate of the probability of exporting infected individuals from sites affected by a disease outbreak to other areas in the world through the airline transportation network and the daily commuting patterns. It also lets the user to explore the effects of potential restrictions applied to airline traffic and commuting flows.
Based on the number of infected individuals detected in one or more areas of the world, the following quantities are computed.
· Relative importation risk: the platform estimates the conditional probability of an infected individual traveling from the source locations to a given destination with respect to any other possible destination.
· Exported cases: the tool evaluates the probability distribution that a given number of infected individuals leave the areas where the outbreak occurs.
· Source cases: assuming exported cases are detected abroad, the platform calculates the likelihood of a range of values corresponding to the number of infected individuals in a given source country.
By interacting with the map, the user can inspect the relative risk and the probability distribution of exported cases for single locations. In addition, it is possible to download the computed results according to commonly used data formats and as a high-resolution image of the risk map.
The platform uses airline transportation data based on origin-destination traffic flows from the OAG database and aggregated at specific temporal and spatial scales by the GLEAM project. Commuting flows are derived by the analysis and modeling of data corresponding to more than 5,000,000 commuting patterns among 78,000 administrative regions in five continents.
EpiRisk is a not-for-profit platform: the results generated by the tool can be shared in compliance with the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
We consider that the outbreak of an infectious disease is taking place in one or more cities (or countries). The relative risk associated with a given city (or country) is the conditional probability that an infectious individual arrives there with respect to any other possible destination.
We assume that infected individuals can travel outside of the source cities (or countries), where the outbreak is occurring, until they begin to show symptoms. The daily probability of developing clinical signs is determined based on the disease's average time from infection to symptom onset.
To compute the relative risk, we developed a method that allows considering multiple sources and combines two different kinds of mobility networks: origin-destination flight flows based on real-world seasonal air traffic data, and daily commuting patterns among neighboring cities. In addition, it is possible to specify a particular travel level to consider potential travel restrictions.
The model is also pretty flexible regarding the information about the infected individuals. Indeed, it allows to compute the relative risk of a particular destination by specifying the exact number of cases in every source city (or country) considered, but also to get an estimate when just the overall number of infected individuals is given, or even if it is unknown, leveraging the mobility data.
Assuming an outbreak of an infectious disease is taking place in a specific source country, the probability distribution P([Ns1, Ns2] | Ne) represents the likelihood of having a number of infected individuals in the bin [Ns1, Ns2] when Ne exported cases are detected abroad. The potential underreporting of exported cases is taken into account by using an appropriate detection efficiency value.
We consider that infected individuals can travel abroad until they begin to show symptoms. Each individual has a daily probability, Ps, of developing clinical signs, which is determined based on the disease's average time from infection to symptom onset. The daily probability of traveling abroad, Pt, is calculated using flight outflows from the source country (based on real-world seasonal air traffic data) and a travel level that accounts for potential travel restrictions. Using Ps and Pt, the total exportation probability Pe for each infected individual is calculated as:
Pe = Pt (1 - Ps) / (Ps + Pt - Ps Pt).
Assuming there are Ns source cases traveling abroad independently from each other, the probability of having Ne exported individuals is given by the binomial distribution B(Ns, Pe; Ne) with parameters Ns and Pe.
To determine the source cases' probability distribution P([Ns1, Ns2] | Ne), one must evaluate B(Ns, Pe; Ne) for every possible value of Ns within each bin [Ns1, Ns2]. Leveraging the properties of the binomial distribution, we developed an efficient adaptive method to automatically identify a relevant range of source cases where the probability B(Ns, Pe; Ne) significantly deviates from zero. This method requires minimal computations of the binomial. The source cases' probability distribution is then obtained by dividing the relevant range into an appropriate number of bins, estimating the sum of B(Ns, Pe; Ne) for each bin using a midpoint integration rule, and finally renormalizing the overall distribution.
Special care has been taken regarding the implementation of the numerical procedures, in particular with respect to the correct handling of edge cases and the behavior when there are only a few exported cases (or even zero), which may result in an extremely skewed probability distribution.
We consider that the outbreak of an infectious disease is taking place in one or more cities (or countries). The distribution of exported cases gives the probability that a certain number of infected individuals leave the cities (or countries) where the outbreak occurs. In a similar way, it is also possible to compute the probability distribution that a given number of exported cases arrive at a specific destination.
We assume that infected individuals can travel outside of the source cities (or countries) until they begin to show symptoms. The daily probability of developing clinical signs, Ps, is determined based on the disease's average time from infection to symptom onset.
The daily probability of individuals traveling outside the source location, denoted as Pt, is calculated using two distinct mobility networks. The first is origin-destination flight flows derived from actual seasonal air traffic data. The second comprises daily commuting patterns among nearby cities. Moreover, one can adjust for a specific travel level to account for potential travel restrictions.
Knowing Ps and Pt enables us to calculate the total exportation probability, Pe, of each infected individual in a given source. Assuming there are Ns source cases traveling independently from each other, the probability of having Ne exported individuals from a given source location can be represented by the binomial distribution B(Ns, Pe; Ne) with parameters Ns and Pe.
To compute the overall probability distribution of exported cases, P(E), it is necessary to consider the contribution of each source city, or country, to the total number E of exported infected individuals. This means aggregating the discrete random variables corresponding to the binomial distributions B(Ns, Pe; Ne) from each source. From a computational point of view, this would in principle require a number of operations that grows exponentially with the number of sources. To circumvent this problem, we have devised an efficient method to calculate the distribution P(E) of exported cases: by summing the random variables using a recurrence relation and truncating the binomial functions for values that don’t significantly deviate from zero, we can limit the number of required operations to grow almost linearly with the number of sources.
Our model is adaptable and accommodates varying degrees of information about infected individuals. It can compute the distributions of exported cases by using either the exact count of infected individuals in every considered source city or country, or by simply providing the total number of source cases.
Top destinations ranked according to the relative risk of case importation
Probability distribution of case exportation
Estimated probability distribution