Estimating the probability of dengue virus introduction and secondary autochthonous cases in Europe

Given the speed of air travel, diseases even with a short viremia such as dengue can be easily exported to dengue naïve areas within 24 hours. We set out to estimate the risk of dengue virus introductions via travelers into Europe and number of secondary autochthonous cases as a result of the introduction. We applied mathematical modeling to estimate the number of dengue-viremic air passengers from 16 dengue-endemic countries to 27 European countries, taking into account the incidence of dengue in the exporting countries, travel volume and the probability of being viremic at the time of travel. Our models estimate a range from zero to 167 air passengers who are dengue-viremic at the time of travel from dengue endemic countries to each of the 27 receiving countries in one year. Germany receives the highest number of imported dengue-viremic air passengers followed by France and the United Kingdom. Our findings estimate 10 autochthonous secondary asymptomatic and symptomatic dengue infections, caused by the expected 124 infected travelers who arrived in Italy in 2012. The risk of onward transmission in Europe is reassuringly low, except where Aedes aegypti is present.

vectors during the summer season when vectorial capacity is sufficient to sustain transmission and (2) the rate of dengue virus importations, that depends on the number of dengue viremic travelers entering Europe. Most of the modeling work has been focused on understanding the risk of local transmission and relatively little attention has been given to the extent of disease importations. As human movements resulting in global spread of infectious diseases including vector-borne diseases are increasing [9][10][11][12][13][14][15][16][17][18] and the burden of diseases such as dengue increases, we can expect an exponential increase in arrivals of viremic passengers which may challenge traditional health infrastructures.
Given the speed of air travel today 19 and increase of travel to tropical and subtropical countries 19 , diseases with short viremia such as dengue (around 7 days) can be easily exported to a dengue naïve areas within 24 hours, where mosquitoes may then be able to feed on viremic blood, and transmit the virus on to other humans. A sentinel surveillance study recently estimated that about 40% of travelers diagnosed with dengue are viremic at the time of arrival in Europe 20 . The first large dengue outbreak in Europe that occurred in Madeira in 2012 as a result of importation of the virus via incoming viremic air passengers most likely from Venezuela 8 prompted us to study the extent of potentially dengue viremic travelers arriving in Europe as a whole in the same year and to estimate the probability of secondary transmission in Europe as a result of such importation. In the absence of good empiric data on importation of dengue via viremic travelers, mathematical models can provide an additional tool to estimate the number of dengue virus introductions 21 . The extent of dengue virus introduction is a function of travel volume and dengue incidence in the 'exporting' country 22,23 . We set out to model the estimated numbers of dengue-viremic air passengers from dengue-endemic countries to 27 European countries and the subsequent risk of autochthonous transmission as a result of such importation.

Methods
We applied a previously published mathematical model to estimate the risk of importation of infectious diseases via travelers 21 , and expanded it to further to include models on vectorial capacity 4,5 . To estimate the number of dengue viremic air passengers into Europe in one year we took into account air travel volume, the dengue monthly incidence in the country of origin, and the probability for the air passenger to be viremic at the time of travel.
We consider two types of countries, the 'exporting' country (where the infection is endemic) and those 'importing' or 'receiving' countries. We investigated the number of imported dengue-viremic travelers into 27 European countries based on the following variables: (1) the monthly dengue incidence in the exporting countries; (2) the monthly number of people leaving the airports of exporting countries and traveling to importing countries; (3) the expected monthly number of dengue-viremic travelers arriving at the importing countries. (4) the accumulated number of secondary cases in humans in the importing countries generated by the infected travelers from the exporting countries taking into account the vectorial capacity of Aedes mosquitoes in the importing countries over a one year period; and (5) the accumulated per capita risk of dengue infection in the population of the importing countries over one year caused by infected travelers arriving in that year. Items 4 and 5 will be exemplified by the cases of Italy, in which Aedes albopictus is currently present, and Madeira, where Aedes aegypti caused an important outbreak in 2012. Aedesalbopictus is a much less competent mosquito for dengue  Estimating the incidence of dengue in the exporting countries. The first step was to obtain information on dengue cases notified to the World Health Organization (WHO) from their website (www.who.int). From the 85 countries that reported 1,597,220 dengue cases to WHO in 2012 we selected 16 countries which were responsible for 95% of all the cases. These countries, along with the number and relative contribution to the total number of dengue cases are shown in Table S1 (supplementary material). Of these 16 selected countries, 9 are from South and Central America, and the rest from Asia. As cases are only reported to WHO on an annual basis, we inferred the seasonal distribution per month from those two countries where we had monthly data: Brazil and Thailand. We assumed that the 9 South and Central American countries had seasonality similar to that of Brazil. The remaining 7 Asian countries were assumed to have the same seasonality as Thailand. The seasonal pattern of these two reference countries, Brazil and Thailand, are shown in figures S1 to S4 (supplementary material). We assumed that visitors to the exporting countries were subject to the same risk of infection as the local inhabitants.
Estimating the monthly number of people leaving the airports of exporting countries and traveling to importing countries. The second step is to fit a continuous function to the number of actually reported dengue cases (incidence) multiplied by 4 to take into account the 4:1 asymptomatic:symptomatic ratio for dengue infections 24 . The continuous function chosen has the form: representing the time-dependent dengue infection incidence. In equation (1) c 1 is a scale parameter that determines the maximum incidence, c 2 is the time at which the maximum incidence is reached, c 3 represents the width of the time-dependent incidence function and c 4 is a time and location dependent parameter to counter the seasonal differences in dengue incidence between Northern and Southern Hemisphere. Equation (1) reproduces a "Gaussian" curve and so c 1 and c 4 are just scale parameters but c 2 crepresents the "mean" (and mode or maximum) time and c 3 represents the "variance" of the time distribution of cases. All parameters c 1 ,i = 1, …, 4 fitted to function (1), when used in the dynamical model described below reproduces the observed incidence of dengue for a given outbreak in a region preferably small as we will explain later. Parameter c 4 is given by: where rect (t) is a rectangular function added to equation (1) to take account of the slight increase in the risk at the end of the year in the Southern Countries (summer time). The rectangular function is a square pulse of determined duration and can be written in terms of the Heaviside step function as θ(t + t i ) − θ(t − t i ). The rect (t) is zero for any t > |t i | and is equal to 1 for t < |t i |. The number of monthly reported dengue cases of all 16exporting countries, was used to estimate the monthly prevalence of dengue in each country. Therefore, all the quantities should have a superscript j (j = 1 … 12) denoting the months of the year. We used previously developed and validated models (1) and (2)  ) models the number of new infections per time unit. In terms of the classical notation of vector-borne infections 27 it is equal to the product of the force-of-infection, λ j (t) times the number of susceptible humans, denoted S t ( ) H j . As is well known, the force-of-infection in vector-borne infections is the product of the biting rate times the probability of transmission from infected mosquitoes to the human hosts, times the number of infected mosquitoes divided by the total number of humans 27 .
The individual probability of being infected at time t, defined as the monthly individual risk of being infected and denoted Risk t ( ) DENV j , which is given by the prevalence of dengue: This risk is obtained as follows. From the second equation of model (3) for the infected humans we obtain: Note that the concept of risk expressed in equation (4) means the probability of finding at least one dengue case at month j, either among travellers who visited each of the selected countries or among local inhabitants. In addition, equation (4) includes the notion that a proportion of the infected individuals can recover from the infection or die after they arrive at one of the European countries.
Estimating the number of dengue-viremic air passengers arriving in the importing countries. We obtained the expected number of passengers arriving in European countries infected with dengue in the exporting countries by multiplying equation (4)  Estimating the monthly number of secondary dengue infections in humans in the importing countries generated by dengue-viremic travelers from the exporting countries based on vectorial capacity in that country. In order to estimate the monthly number of autochthonous mosquitoes and humans we used again the Ross-Macdonald in its full version.
Infected (i.e., dengue-viremic) travellers arrive at each month j of the year and are denoted In the model we denote the mosquitoes densities as m t ( )  Note that both the humans' and mosquitoes' populations are assumed to be constant and the last terms of the susceptible humans and susceptible mosquitoes are included to mimic births as equal to deaths. This is based on the assumption that dengue does not have any significant impact in humans nor mosquitoes in terms of mortality.
The values of the pulse-like parameters are given in 4 . For the sake of clarity, let us exemplify how the parameters in model (7) enter the code.Let us take the biting rate, for instance, a j (t). As shown in 4 , it varies with temperature and hence with time, that is, it varies seasonally. Its value should be written as a where A j is the value of the biting rate obtained from 4 for the month j. In other words, the biting rate assumes 'discrete' values in each month of the year.We did these calculations for Italy only where we used the average temperature month-by-month and applied the parameters from , were obtained by numerically simulating model (7). The above calculation is restricted to the autochthonous cases generated exclusively by infected travellers. If one is interested in the total number of dengue cases one should substitute the fourth and fifth equations of model (7) Figure 2 shows the countries that present more than 80% of the dengue burden (16 dengue endemic countries). Table 1 provides the probability of an air passenger being dengue viremia at the time of travel from the selected 16 exporting countries with the highest dengue incidence in the world to the 27 European destination countries for every month in the year 2012. Table 2 shows the expected number of dengue viremic air passengers from each of the 16 exporting countries, stratified by country of disembarkation and by country of arrival. Table 3  Autochthonous transmission as a result of dengue virus importation. The risk of onward transmission via Aedes mosquitoes depends on the presence of such mosquitoes, and Fig. 1 shows the Aedes albopictus distribution in Europe. From Fig. 1 it is evident that only Italy has nationwide presence of Aedes albopictus. As the air passenger flight information was available only at a country level, we were only able to calculate the probability of onward transmission where the presence of Aedes albopictus is countrywide. Hence, we selected Italy to illustrate the method to calculate the number of secondary autochthonous cases in one year as a result of dengue virus importation via incoming air passengers from dengue endemic countries. Table 3 shows the monthly number of dengue viremic air passengers arriving in Italy. Of the total number of 124 infected travellers to Italy in one year, 51 arrived in the summer months of June, July and August, a seasonal window with the most suitable vectorial capacity for Aedes mosquitoes based on previous calculations on the seasonal variation of vectorial capacity in different European cities by Liu-Helmersson et al. 4 . Out model estimated that 10autochthonous (secondary) cases would occur as a result of 51 air passengers arriving in Italy at a time of being dengue viremic. These 10 persons include 2 (20%) symptomatic dengue cases, assuming a 4:1 ratio of asymptomatic to symptomatic infections. We also validated our models against the well-documented dengue outbreak in Madeira with 2180 reported dengue cases. We estimated the risk of autochthonous transmission for the Madeira Islands where Aedes aegypti   (4) Table 4 summarizes the cumulative per capita risk and expected number of autochthonous cases for Italy (Aedes albopictus) and the Madeira Islands (Aedes aegypti). The parameters used for the simulations can be found in Table S2 (Aedes albopictus) and S3 (Aedes aegypti) of the supplementary material.

Discussion
Although reported autochthonous cases in Europe in the recent past highlight the threat of dengue to Europe 27 , the extent of such a threat has not been quantified. This is the first attempt to quantify the actual number of dengue viremic air passengers from dengue endemic countries into Europe -an important parameter that determines the risk calculations of subsequent local dengue virus outbreaks. As not only clinically apparent viremic cases transmit dengue viruses 28 , we also included asymptomatic infections into our calculations at a published ratio of 4:1. Our estimated number of importations tally with the reported importations of dengue in Europe, although the numbers are slightly lower as we are focusing only on air passengers traveling to Europe still in the viremic phase (e.g. persons traveling at a time of viremia for the short period within 5 days after onset of symptoms) 20,29 . The majority of dengue cases reported in returning travelers to Europe are not viremic anymore at the time of arrival 20 .
The highest number of dengue virus importations via air travelers were modeled to occur in Germany, France and the United Kingdom. Aedes albopictus was recently introduced to Kent, United Kingdom but its distribution is very limited and not yet established 30 . In Germany, many more Aedes albopictus have been reported and established populations have been recorded in parts of Southern Germany 2,31 . However, risk for local transmission is limited under current climatic conditions. Both France and Italy receive a significant number of modeled dengue infected air passengers and both countries have significant presence of Aedes albopictus-indeed France experienced autochthonous dengue transmission in the year 2010 in Nice in the Southern part of its country 7 and Italy experienced a chikungunya outbreak in 2007 in the Northern part of Italy 32 . We were limited to passenger flight information at a country level, so we restricted our analysis of the risk of onward transmission of dengue to Italy, a country where Aedes albopictus is distributed across the majority of the country.
For Italy, we modeled the probability for an imported case to result in secondary cases by taking into account the monthly vectorial capacity where transmission is most suitable (eg the summer months of June, July and August) 4 . We translated these findings into per capita probability in Italy. The per capita probability was as low as 0.000000167, and we estimated 10 secondary infections which include around 2 symptomatic cases. For Madeira, we modeled the probability of an imported case to result in secondary cases to be 0.035 and the expected number of secondary cases to be 2205. The difference in the mosquitoes' species between Italy and Madeira is crucial in appreciating the risk difference between the two countries/areas. As Aedes albopictus is a much less competent mosquito for dengue transmission than Aedes aegypti, a large number of imported infections to Italy resulted in a small number of autochthonous cases, whereas a very small number of imported infections to Madeira resulted in a major outbreak.
Our models have several limitations: From an empirical point of view, there is a need for accurate data on dengue incidence in the origin countries. We relied on notified dengue cases to WHO, which is probably a significant underestimate as recent modeling estimates showed at least 10 to 100 fold higher numbers 33 . Another  limitation is the timing of imports. Here we were restricted to two countries as reference points for fitting monthly incidence curves. However, the highest uncertainties in our model were related to mosquito densities in Europe.
There are no published data on the Aede smosquito abundance in relation to the host population which is a crucial parameter for modelling, nor is there sufficient information on biting rates, extrinsic incubation period, mosquito longevity under temperate climate conditions except for some pivotal temperature driven data derived from the work by Louis Lambrechts' team at the Institute Pasteur 34,35 . We selected the year 2012 for our model parameters (dengue incidence in originating countries and air travel volume) in order to validate our model against the actual dengue outbreak that took place in Madeira in that year. Validating our model against the reported dengue outbreak in Madeira in 2012, we found that our model fits very well with the true number of cases reported: our model results estimated 2205 autochthonous infectious, which is well in agreement with the 2180 reported cases in the 2012 outbreak. Therefore, despite its limitations, the model proposed here can be very useful in the understanding of the risk of dengue virus importation into still unaffected areas, and calculate the probability of secondary cases in those areas where susceptible Aedes mosquitoes exist. This paper is hence intended mainly as a novel methodological proposal to estimate the risk of dengue introductions into Europe and subsequent probability and numbers of secondary (eg locally transmitted) infections.
In conclusion, our estimates highlight that the risk is overall low which probably represents a good approximation of reality.