The number of travel-acquired dengue infections has been on a constant rise in the United States and Europe over the past decade. An increased volume of international passenger air traffic originating from regions with endemic dengue contributes to the increasing number of dengue cases. This paper reports results from a network-based regression model which uses international passenger travel volumes, travel distances, predictive species distribution models (for the vector species), and infection data to quantify the relative risk of importing travel-acquired dengue infections into the US and Europe from dengue-endemic regions. Given the necessary data, this model can be used to identify optimal locations (origin cities, destination airports, etc.) for dengue surveillance. The model can be extended to other geographical regions and vector-borne diseases, as well as other network-based processes.
Dengue is the most common mosquito-borne viral diseases in the world [
The causal agent for dengue is a virus that is transmitted from person to person through the bite of infected
At present, there is no epidemiological surveillance on a national scale in Europe or at the state level in the U.S. [ Development of a model that allows quantification of the risk of dengue importation through specific air travel routes, thus identifying locations at which surveillance systems can optimally be implemented. Prioritization of the type of data collection efforts that must be undertaken to enhance the predictive accuracy of such models.
Given the requisite data, our model can be used as a prediction tool for assessing the risk of importing dengue-infected humans or vectors via air travel based on origin-destination pairs as well as to analyze the effects of changes in passenger travel routes and volumes on spatial patterns of infection spread.
The model compounds all modes of dengue infection which can be caused by four virus serotypes (DENV-1, DENV-2, DENV-3, and DENV-4), and can range in clinical manifestation from asymptomatic infection to severe systemic disease [
Although dengue is now rare in the U.S. and Europe, the mosquito vectors are still present. At least one of the two major vector species,
Thus, imported cases of dengue via international travel may potentially result in establishment of an autochthonous disease cycle and new regional outbreaks in both the U.S. and Europe. This can occur in at least two ways: (i) locally established mosquito populations become infected from new hosts (infected travelers) and then spread the disease; or (ii) mosquitoes carrying the virus arrive at a new environment suitable for them. This threat was exemplified recently in Key West, Florida, which experienced sizeable local outbreaks of autochthonous dengue transmission in 2009-2010 [
Epidemics of dengue, their seasonality, and oscillations over time, are reflected by the epidemiology of dengue in travelers [
Various studies have been conducted to identify the highest travel risks. One survey conducted by the European Network on Imported Infectious Disease Surveillance program [
Tatem et al. [
Our analysis quantifies the relative risk of dengue infected (air travel) passengers entering currently nonendemic regions in the U.S. and Europe at which dengue cases have been recorded. However, it does not include the importation of infected vectors since the influence of that possibility is yet to be established [
Nearly all dengue cases reported in the 48 continental U.S. states were acquired elsewhere by travelers or immigrants. From January 1996 to the end of December 2005, 1196 cases of travel-associated dengue were reported in the continental U.S. [
Further complications arise from the severe underestimation of dengue cases due to underreporting and passive surveillance in both endemic and non-endemic regions. In tropical and subtropical countries where dengue fever is endemic, under-reporting may be due to misdiagnosis, limitations of the standard World Health Organization (WHO) case classification, and lack of laboratory infrastructure and resources, among other factors [
The species distribution models required data on the geographical occurrence of
The required data for the network model were as follows. Disease data: annual infection reports for dengue-endemic countries, non-endemic European countries and U.S. states. Transportation data: passenger air traffic volumes for all flights originating from endemic regions and destined for Europe or the U.S. Spatial data: the corresponding distances for all travel routes.
Unliess explicitly indicated otherwise, the data used in this model were from 2005, and aggregated to the annual level.
The set of dengue-endemic countries was as identified by the CDC [
Difficulties were encountered in acquiring the necessary infection data. First, surveillance data for dengue in Africa were sparse. Even though all four dengue virus serotypes have been documented there [
Transportation data were obtained from two sources. The U.S. air traffic data were from the Research and Innovative Technology Administration (RITA), a branch of the U.S. Department of Transportation (U.S. DOT), which tracks all domestic and international flights originating or ending in the U.S. and its surrounding regions [
The average distances used in the model were calculated in ArcGIS 9.3. The average distances were computed for each route as the geodesic distance between the geographic centers of each region.
The risk for the establishment of dengue and potential cases of disease in an originally non-endemic area depends fundamentally on the ability of a vector to establish itself in that area. If the vector can establish itself then the disease can become endemic in two ways: (i) if the vector is already established, it can become infected from a person infected with dengue arriving in that area; or (ii) infected vectors can be transported into such an area and establish themselves. For this process, habitat in that area must be ecologically suitable for that vector. A relative measure of the suitability of one area compared to another defines a measure of the relative ecological risk [
The analysis here was based on habitat suitability for the two principal dengue vector species,
The output from Maxent consists of relative suitability values between 0 and 1 which, when normalized, can be interpreted as the probabilistic expectation of vector presence of a species in a cell. The probabilistic expectation of at least one of the vector species being present in a cell was calculated as the complement of the probability that neither is present, assuming statistical independence. Because the infection and travel data used in this work are at the state level for the U.S. and the country level for Europe, the expectations are aggregated to the same level by averaging them over all the cells in the relevant geographical units. These expectations define the relative ecological risk for dengue in each cell.
The network model predicts the expected number of dengue cases in each non-endemic region that can be attributed to a particular endemic region connected to it by travel. Two previous mathematical models quantifying risk estimates for acquiring arboviral infection are by Massad and Wilder-Smith [
Our model has similarities to a feedforward artificial neural network (ANN). Feed-forward ANNs have been used to model learning input-output systems, and can be calibrated through a “back-propagation” algorithm that minimizes a cost function representing output error [
In the proposed network structure, geographic areas were represented as nodes, belonging to either the set
This directed bipartite network structure connected endemic countries to susceptible regions (U.S. states and E.U. countries). Initially a single model was developed which included all susceptible regions as a single set of destination nodes,
(a) Bipartite network connecting endemic regions to susceptible regions: the susceptible U.S. and Europe nodes represent mutually exclusive sets; (b) link-based functions: these predict the number of infections at susceptible node A, attributed to each adjacent endemic region (1, 2, and 3).
Figure
The most critical issue was determining the functional form of
The notation used in the formal problem formulation is shown in Table
Problem Notation.
Subset of susceptible nodes in the United States | |
Subset of susceptible nodes in Europe | |
Complete set of susceptible nodes ( | |
Set of nodes in the endemic region | |
Number of reported infections at node | |
Total number of predicted infections at node | |
Number of predicted infections at node | |
Vector of parameter to be optimized | |
Vector of characteristics of infecting node | |
Vector of characteristics of susceptible node | |
Vector if parameters specific to link ( | |
Normalized passenger air travel volume between nodes | |
Climate suitability of node | |
Normalized reported infections at node | |
Normalized distance between nodes | |
Set of endemic nodes adjacent to susceptible node | |
Parameters to be optimize |
The purpose of this analysis was to examine a variety of families of functions, further explore the most suitable member of each family, and examine the results from a qualitative perspective. The objective was to find the parameter vector
Depending on the functional form of
The motivation for the final functional form,
The square root of
By rewriting the original mathematical program in terms of the node based variables
The main objective of the model was to quantify the relative risk of various international travel routes. This was accomplished by first predicting the number of dengue cases specific to each travel route, and then calibrating the network model at a regional level using infection data. Therefore, there are two sets of results presented. Section
The results included in this section are representative of filtered data. The filtering process was applied to the susceptible node set to remove outliers. The outliers were classified differently for the European and U.S. node sets. In the European data set any region with less than 5 cases was considered an outlier, while only states with one reported case were considered outliers in the U.S. node set. A lower threshold was implemented for the U.S. as there were fewer reported cases on average. The procedure resulted in five nodes being removed from
The model was able to predict closely the number of reported cases for the European countries, though it struggled to predict the number of reported cases for the U.S. states accurately. The results for the node-based predictions,
Model output and actual reported infections for (a) Europe and (b) the US
Infections for susceptible European countries.
E.U. country | Actual reported infections | Model reported infections |
---|---|---|
Belgium | 25 | 31 |
Czech Republic | 9 | 31 |
Finland | 12 | 40 |
France | 300 | 247 |
Germany | 204 | 231 |
Sweden | 61 | 55 |
United Kingdom | 170 | 196 |
Total | 781 | 831 |
Infections for susceptible U.S. states.
U.S. State | Actual Reported Infections | Model Reported Infections |
---|---|---|
Hawaii | 11 | 6 |
Massachusetts | 14 | 12 |
New York | 55 | 22 |
Pennsylvania | 3 | 11 |
Florida | 22 | 24 |
Georgia | 7 | 16 |
North Carolina | 5 | 9 |
Virginia | 5 | 6 |
Illinois | 3 | 14 |
Ohio | 4 | 6 |
Wisconsin | 2 | 4 |
Minnesota | 11 | 6 |
Texas | 24 | 20 |
Arizona | 5 | 4 |
Nevada | 2 | 7 |
California | 4 | 22 |
Oregon | 4 | 4 |
Washington | 6 | 5 |
Total | 187 | 196 |
The functional form introduced in Section
Several factors contributed to complicating the task of identifying a function to perfectly fit the case data. Firstly, the limited size of the susceptible node set made it difficult for the model to differentiate between variability and noise. Secondly, the amount of noise in the data due unknown factors such as variations in regional surveillance efforts could not be accounted for. Thirdly, prevention measures being implemented were not only difficult to determine, but also difficult to quantify. All these uncertainties restricted the model’s ability to estimate parameters that resulted in good predictive properties at the node level. However, our results show that, though the fit at the node level could be improved upon, the route-level risk measures do show promising results, and as such, provide some insight into the role the independent variables play.
Although the node-based predictions can be validated based on the reported infection data, the resulting route-based predictions were not directly-verifiable due to the unavailability of route-based infection data. The best measures of validation were (i) to find route-based predictions that correspond to known regional infection data when summed across all incoming routes, and (ii) to compare the results with previous travel-based patient surveys conducted to determine the most likely place of origin for illness.
Table
Relative risk of spreading travel acquired dengue infection via international travel routes from endemic countries into (a) Europe and (b) US
Route-based relative risk european countries.
Rank | From | To | Relative Risk |
---|---|---|---|
1 | Brazil | Germany | 1.00 |
2 | Brazil | France | 0.99 |
3 | South East Asia | Germany | 0.71 |
4 | South East Asia | United Kingdom | 0.52 |
5 | Brazil | United Kingdom | 0.35 |
6 | South East Asia | France | 0.29 |
7 | Vietnam | France | 0.29 |
8 | Singapore | United Kingdom | 0.27 |
9 | Singapore | Germany | 0.19 |
10 | India | Germany | 0.19 |
11 | Malaysia | United Kingdom | 0.19 |
12 | India | United Kingdom | 0.17 |
13 | Dominican Republic | Germany | 0.16 |
14 | Venezuela | Germany | 0.16 |
15 | Dominican Republic | France | 0.16 |
16 | Mexico | France | 0.16 |
17 | Mexico | Germany | 0.15 |
18 | Venezuela | France | 0.15 |
19 | South East Asia | Finland | 0.14 |
20 | South East Asia | Sweden | 0.13 |
Route-based relative risk for U.S. states.
Rank | From | To | Relative risk |
---|---|---|---|
1 | Mexico | Texas | 1.00 |
2 | Mexico | California | 0.56 |
3 | Puerto Rico | Florida | 0.34 |
4 | Brazil | Florida | 0.33 |
5 | Venezuela | Florida | 0.24 |
6 | Mexico | Illinois | 0.23 |
7 | Puerto Rico | New York | 0.21 |
8 | Costa Rica | Florida | 0.19 |
9 | Mexico | Florida | 0.19 |
10 | Mexico | Arizona | 0.19 |
11 | Dominican Republic | New York | 0.17 |
12 | Colombia | Florida | 0.16 |
13 | Brazil | New York | 0.15 |
14 | Mexico | Georgia | 0.15 |
15 | Dominican Republic | Florida | 0.15 |
16 | Brazil | Texas | 0.14 |
17 | Brazil | Georgia | 0.12 |
18 | Honduras | Florida | 0.12 |
19 | Costa Rica | Texas | 0.12 |
20 | Mexico | Nevada | 0.11 |
Figure
(a) The 20 highest traveled routes entering the U.S. and E.U. There are 40 total links; the line thickness is proportional to the travel volume. (b) The top 20 travel routes with highest relative risk of carrying Dengue infected passengers into U.S. and E.U. The line thickness is proportional to the relative risk of the route.
As stated previously, one way to verify the predicted route-based risk was by comparing the results with previous patient surveys conducted to identify the source of infections. A previous study found of the travel acquired dengue cases in Europe between 1999 and 2002 [ 219 (45%) originated in South-East Asia, represented in the model as 3 of the top 6 highest risk routes, 91 cases (19%) originated in South and Central America, represented in the model as 3 of the top 10 highest risk routes, 77 cases (16%) originated in the Indian subcontinent, represented in the model as 2 of the top 15 highest risk routes, 56 cases (12%) originated in the Caribbean, represented in the model as 2 of the top 20 highest risk routes.
The model predicted Brazil-Germany and Brazil-France as the two highest risk routes into Europe (with nearly equivalent relative risk). This is expected, as Brazil reported the highest number of dengue cases in the world per year, almost 3-times those of second place Indonesia, and the volume of traffic on the Brazil-France and Brazil-Germany routes were two of the top 40 in the world. Indonesia, reported a very high number of infections, but reported a very low level of air travel on any given route destined for Europe. Using similar logic, Southeast Asia reported a number of infections on par with Indonesia, though the travel volume from Southeast Asia into Germany and the United Kingdom ranked among the world’s top 25 travel routes; suggesting intuitively that travel volume is a dominant factor in assessing infection risk.
For the U.S. the model predicted the majority of U.S. infections were attributed to Central and South American countries, likely a result of the close proximity, high traffic, and high level of infection. More specifically, 19 of the top 20 highest risk routes into the U.S. (Nevada, ranked 20th not included) were destined for states which account for a very high fraction of incoming flights in the US; accounting for 6 of the top 15 busiest American Airports by boardings [
As a destination, Florida accounted for 5 of the top 10 risk routes, which is supported by historical occurrence of the disease, exemplified in the 2009-2010 local outbreaks. Though it is possible that dengue was already present in the locality (Key West), and previously undetected, the results of this model suggest dengue was likely introduced via international travelers into a locality with environmental and social conditions ripe for transmission [
Mexico-Texas and Mexico-California ranked as the two highest risk routes, and were also the top two traveled routes (by passenger volume) in the world [
Dengue currently presents a serious risk to many parts of the U.S. and Europe where suitable environmental conditions for vector species’ occurrence and establishment provide the potential for local outbreaks, were the virus to be introduced. The background to this analysis was the increasing number of dengue cases in the U.S. and Europe, coinciding with an increase in both the prevalence of dengue worldwide and increased volume of international passenger air traffic originating from dengue-endemic regions since the 1990s.
The model presented here was developed to explore the relationship between reported dengue infections and air travel. It used a network-based regression to quantify the relative risk from international air travel routes carrying infected passengers from endemic regions to non-endemic ones in the U.S. and Europe. Besides international passenger travel volumes, the model incorporated predictive species distribution models for the principal vector mosquito species. The model also incorporated travel distances and infection data. The following inferences follow from the model results. The highest-risk travel routes suggest that the proximity to endemic regions is a dominant factor. Most high-risk routes into Europe originate in Asia (with the exception of Brazil and Mexico), while all top 20 routes into the U.S. originate in South and Central America. Travel from dengue-endemic countries presents significant risk to Florida. Additionally, the high volume of domestic visitors to Florida in conjunction with established The high risk predicted for Mexico-Texas travel is further heightened by the risk of overland transmission (such as that from Tamaulipas into the Brownsville area [ For many countries of Europe and U.S. states, if dengue gets introduced, the establishment of an autochthonous disease cycle is likely because many of these areas contain suitable habitats for Some of the “source” areas indicate that dengue has yet to be brought under control in places where malaria has. This means that dengue may well replace malaria as the paradigmatic airport disease.
The results provided in this paper were obtained using existing (historical) data from the (recent) past and do not represent fully reliable predictions for relative risks in the future. However, the model introduced in this paper can be calibrated using epidemiological data from any time period. The calibrated model can be used as a predictive tool for quantifying route-based risk in the future provided that the necessary data are available, including real-time travel patterns, environmental conditions, and infection data. Moreover, the results in this paper are aggregated at the annual and regional (country or state) level due to the limitations of available data. Infection data proved to be the most difficult to gather because infection reports for many regions in the world are not available even at the annual level. Appropriate data will enable the extension of the model to allow analysis at finer spatial and temporal resolutions: the model can be regionally disaggregated to the city level, or disaggregated by month to account for seasonality. Moreover, this model can be deployed in other geographical regions, used for other vector-borne diseases, and modified to analyze other network-based processes. Finally, this model can potentially be extended to include other modes of transportation, such as freight and shipping networks.
The development of such models is an integral step in improving local and regional surveillance efforts. The quantitative results produced by the model can lead to more specific surveillance recommendations than the CDC is currently able to make such as identifying (i) specific routes on which to implement surveillance and control strategies and (ii) optimal locations (origin cities, destination airports, etc.) for passenger surveillance efforts. As there is currently no vaccine for dengue; surveillance and intervention, along with vector control, are the only relevant options to prevent further geographic spread of the disease. The limitations of this analysis highlight the need for improving the quality of readily accessible disease data so as to enhance the prediction and control of epidemic episodes of vector-borne diseases in susceptible countries.