A Global Model for Predicting the Arrival of Imported Dengue Infections

A global model for predicting the arrival of imported dengue infections

Jessica Liebig1,∗ Cassie Jansen2, Dean Paini3, Lauren Gardner1,4,5, Raja Jurdak1,6,7

1Data61, Commonwealth Scientiﬁc and Industrial Research Organisation Brisbane, Queensland, Australia 2Communicable Diseases Branch, Department of Health Brisbane, Queensland, Australia 3Health & Biosecurity, Commonwealth Scientiﬁc and Industrial Research Organisation Canberra, Australian Capital Territory, Australia 4Department of Civil Engineering, Johns Hopkins University Baltimore, Maryland, USA 5School of Civil and Environmental Engineering, University of New South Wales Sydney, New South Wales, Australia 6School of Electrical Engineering and Computer Science, Queensland University of Technology Brisbane, Queensland, Australia 7School of Computer Science and Engineering, University of New South Wales Sydney, New South Wales, Australia

Abstract

With approximately half of the world’s population at risk of contracting dengue, this mosquito-borne disease is of global concern. International travellers significantly contribute to dengue’s rapid and large-scale spread by importing the disease from endemic into non-endemic countries. To prevent future outbreaks and dengue from establishing in non-endemic countries, knowledge about the arrival time and location of infected travellers is crucial. We propose a network model that predicts the monthly number of dengue-infected air passengers arriving at any given airport. We consider international air travel volumes to construct weighted networks, representing passenger flows between airports. We further calculate the probability of passengers, who travel through the international air transport network, being infected with dengue. The probability of being infected depends on the destination, duration and timing of travel. Our findings shed light onto dengue importation routes and reveal country- specific reporting rates that have been until now largely unknown. This paper provides important new knowledge about the spreading dynamics of dengue that is highly beneficial for public health authorities to strategically allocate the often limited resources to more efficiently prevent the spread of dengue.

Introduction tant mosquito-borne disease [11, 12]. The rapid geographic spread is, to a great extent, driven by the increase in inter- The well connected structure of the global air transportation national air travel [13, 14]. In addition, dengue is severely arXiv:1808.10591v3 [q-bio.PE] 11 Nov 2019 network and the steadily increasing volume of international under-reported, making it extremely challenging to monitor travel has a vast impact on the rapid, large-scale spread of and prevent the spread of the disease. Presumably, 92% arboviral and other diseases [1, 2, 3, 4, 5, 6, 7]. A recent ex- of symptomatic infections are not reported to health au- ample of disease introduction to a novel region is the spread thorities [10]. Low reporting rates can have many reasons, of the Zika virus from Brazil to Europe, the United States including low awareness levels and misdiagnosis [9, 15]. and other countries, which prompted the World Health Or- Due to the rapid global spread of dengue as well as se- ganisation (WHO) to announce a public health emergency vere under-reporting, many countries are facing the threat of international concern in early 2016. Investigations con- of ongoing local transmission in the near future [11]. In non- ﬁrmed that international viraemic travellers were a major endemic countries, local outbreaks are usually triggered by contributing factor to the rapid spread [8]. an imported case [16], a person who acquired the disease With an estimated 50-100 million symptomatic infec- overseas and transmitted the virus to local mosquitoes. To tions each year [9, 10], dengue is ranked the most impor- prevent ongoing dengue transmission in non-endemic countries, it is critical to forecast the importation of disease ∗Corresponding author: [email protected] cases into these areas and move from responsive contain-

1 ment of dengue outbreaks to proactive outbreak mitigation and hence are difficult to determine [10]. The usual ap- measures. proach towards estimating country-specific reporting rates The majority of existing models forecast relative rather is to carry out cohort or capture-recapture studies that can than absolute risk of dengue importation and are unable be costly, are time consuming and may be biased [28]. Con- to predict the total number of imported disease cases [13, sequently, dengue reporting-rates remain unknown for most 17, 18]. The few models that can predict absolute numbers countries [10]. are region-specific rather than global [19, 20, 21]. The most In this paper we focus on those countries that are most recently proposed model estimates the total number of im- at risk of dengue introduction, i.e. non-endemic countries ported dengue cases for 27 European countries [21], however, with vector presence. These countries will have the greatest the model has several limitations: (i) Monthly incidence benefit from our model as knowledge about the likely arrival rates were based on dengue cases reported to the World times and places of infected people is crucial to prevent local Health Organisation (WHO) despite dengue being under- outbreaks. reported and the general consensus that the actual number of cases is much higher than the figures published by the Materials and methods WHO [10, 9]; (ii) Only 16 countries were considered as possible sources of importation. The authors reason that these 16 CSIRO’s human research ethics committee CSSHREC has countries contribute 95% of all global dengue cases, referring approved this study (approval number: Ethics Clearance to numbers published by the WHO. Since African countries 142/16). All data were analysed anonymously and individ- do not report to the WHO, and dengue remains an under- uals cannot be identified. reported disease in many other countries [22, 23, 24, 25], it is likely that the percentage contribution to the number of global dengue cases by the 16 selected countries is strongly IATA Data biased; (iii) Seasonal distributions of dengue cases were inferred based on information from only two source countries The International Air Transportation Association (IATA) (Latin American countries were assumed to have similar sea- has approximately 280 airline members who together con- sonalities to Brazil, while Thailand served as a proxy for tribute to approximately 83% of all air traffic. Data is col- countries in South-East Asia). The assertion that all coun- lected in form of travel routes, detailing the origin, destina- tries within a given global region experience similar seasonal tion and stopover airports. It contains over 10,000 airports fluctuations in dengue infections is likely inaccurate. For ex- in 227 different countries and dependencies. For each route ample, dengue notifications peak between April and Decem- the total number of passengers per month is given. We do ber in Thailand, while Indonesia reports the highest number not have any information on stopover times and whether of dengue cases from November to April [26]. passengers are leaving the airport during their stopover and therefore assume that all passengers continue their jour- The contribution of this paper is twofold. First, we de- ney to the final destination instantly. Table S1 lists the velop a network model that overcomes the limitations of IATA 3-Letter Codes used to abbreviate airports in the main previous models by employing global air passenger volumes, manuscript. As the recorded itineraries do not include any country-specific dengue incidence rates and country-specific travel on chartered flights, we compare the IATA passenger temporal infection patterns. We construct weighted directed volumes to official airport passenger statistics [29, 30, 31, networks, using data collected by the International Air 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47] Transportation Association (IATA) to capture the move- to quantify the potential discrepancies between actual travel ment of air passengers. We calculate monthly, country- patterns and that reported by IATA. Table S2 lists the coun- specific dengue incidence rates by combining data from the tries where the difference in passenger numbers is greater Global Health Data Exchange [27], the most comprehensive than 15% (at country level) and countries where airport health database, and known seasonal patterns in reported statistics were not available and the tourist data suggests dengue infections [26]. Further, we distinguish between inaccuracies in the IATA data (i.e. the number of tourists two categories of travellers: returning residents and visi- arriving in a particular country is larger than the total num- tors. The number of days people from these two categories ber of passengers arriving). We also excluded Singapore as a spend in an endemic country, and therefore the risk of being source of importation for Australia for the following reason: infectious on arrival, vary greatly. The model predicts the The Department of Home Affairs publishes Arrival Card number of imported dengue cases per month for any given data [48] that can be used to validate the IATA data. A airport and can be applied with relative ease to other vector- comparison of the monthly travel volume from Singapore to borne diseases of global concern, such as malaria, Zika or Australia revealed that the IATA data overestimates travel chikungunya. volumes by approximately 112% on average in 2011 and Second, we apply the model to infer time-varying, region- 2015. This may be due to individuals who travel from other specific reporting rates, defined as the ratio of reported countries to Singapore and then directly continue to Aus- to actual infections. Dengue reporting rates vary greatly tralia and do not book their entire trip in one itinerary (this across space and time, often by several orders of magnitude, would be recorded as two separate trips in the IATA data

2 that cannot be linked to each other). Due to this large where γc,m is the monthly dengue incidence rate in country discrepancy in the travel data we believe that our model c during month m and dm is number of days in month m. will signiﬁcantly overestimate the number of dengue infec- Note that Equation (1) converts the daily incidence rate tions imported from Singapore, and therefore exclude it as into the probability of a single person becoming infected a source country for Australia. with dengue on any given day during month m.

The air transportation network Inferring the number of infected passengers We begin by constructing twelve weighted, directed net- Next, we present a mathematical model that approximates works, using IATA data, to represent the monthly move- the number of dengue-infected people for each edge in the ment of air passengers during a given year. The networks network Gm(V,E). The time between being bitten by an are denoted Gm = (V,E), with m = 1,..., 12 indicating infectious mosquito and the onset of symptoms is called the the month of the year. The node set V comprises more intrinsic incubation period (IIP). This period closely aligns than 10,000 airports recorded by IATA. To distinguish the with the latent period, after which dengue can be transmit- travellers by their country of embarkation, we represent the ted to mosquitoes [49]. The IIP lasts between 3 and 14 days edges of the network as ordered triples, (i, j, ωi,j(c, k)) ∈ E, (on average 5.5 days) and was shown to follow a gamma where i, j ∈ V and ωi,j(c, k) is a function that outputs the distribution of shape 53.8 and scale equal to 0.1 [50]. Af- number of passengers who initially embarked in country c ter completion of the IIP a person is infectious for approxi- with final destination airport k and travel from airport i to mately 2 to 10 days (on average 5 days) [51, 50]. The length airport j as part of their journey. of the infectious period was shown to follow a gamma distribution of shape 25 and scale equal to 0.2 [50]. We denote the sum of the IIP and the infectious period by n, which Incidence rates and seasonal distributions is rounded to the nearest integer after the summation. For Calculating the number of infected passengers requires daily travellers to import the infection from country c into a new infection probabilities. We derive these from country-level location r they must have been infected with dengue within yearly estimates of symptomatic dengue incidence rates that the last n − 1 days of their stay in country c. We now con- are published together with their 95% confidence intervals sider the following two cases: tc ≥ n − 1 and tc < n − 1, by the Global Health Data Exchange [27]. The estimates where tc is number of days spent in country c before arriving are obtained using the model published in [10] and account in region r. Since we do not know the exact date of arrival for under-reporting. for travellers, we assume that arrival and departure dates We first deduce monthly incidence rates using informa- fall within the same month and hence βc,m is the same for tion on dengue seasonality published by the International every day during the travel period. Association for Medical Assistance to Travellers [26]. To do If tc ≥ n − 1, that is the individual spent more time in so we associate a weight with each month that indicates the country c than the sum of the lengths of the IIP and the intensity of transmission. To assign the weights we use a infectious period, the probability of not being infected on tc tc−(n−1) modified cosine function with altered period that matches return is equal to (1 − βc,m) + 1 − (1 − βc,m) . the length of the peak-transmission season. The function The first term covers the possibility that the individual did is shifted and its amplitude adjusted so that its maximum not get infected whilst staying in country c and the second occurs midway through the peak-season with value equal to term covers the possibility that the individual got infected the length of the peak-season divided by 2π. The months and recovered before arriving at a given airport (see Fig S1). outside the peak-season receive a weight of one if dengue Hence, the probability of a person, who arrives at a given transmission occurs year around and a weight of zero if airport from country c during month m, being infected with dengue transmission ceases outside the peak-season. The dengue is given by weights are then normalised and multiplied by the yearly incidence rate for the corresponding country. Normalising h i tc tc−(n−1) the weights ensures that the sum of the monthly incidence pc,m = 1 − (1 − βc,m) + 1 − (1 − βc,m) rates is equal to the yearly incidence rate. To calculate tc−(n−1) tc = (1 − βc,m) − (1 − βc,m) . (2) the lower and upper bounds of the monthly incidence rates, we multiply the normalised weights by the lower and upper If tc < n − 1, that is the individual spent less time in bounds of the 95% confidence interval given for the yearly country c than the sum of the lengths of the IIP and the incidence rates. infectious period, the probability of not being infected on The average probability, β , of a person becoming in- tc c,m return is equal to (1 − βc,m) , which covers the possibility fected on any given day during month m in country c is then that the individual did not get infected whilst staying in given by country c. Since tc < n−1, the probability of recovery before arriving at a given airport is zero. Hence, the probability −γc,m/dm βc,m = 1 − e , (1) of a person, who arrives from country c at a given airport

3 during month m, being infected with dengue is given by dian population age. Median population ages by country are published in the World Factbook by the Central Intelli- tc pc,m = 1 − (1 − βc,m) . (3) gence Agency [53]. For simplicity we do not take immunity to the different We distinguish between two different types of travellers dengue strains into consideration. arriving at a given airport of region r: returning residents and visitors. We define a returning resident as a traveller who resides in region r and a visitor as a traveller who resides Proportion of returning residents and visitors in country c and visits region r. Returning residents are Lastly, we need to infer the proportions of returning resi- expected to have stayed a couple of weeks in the endemic dents and visitors. As this information is not contained in country, while visitors may have spent their whole life in the the IATA itineraries, we use international tourism arrival country. data from the World Tourism Organisation [54]. The data Since we lack information on how long each individual contains the yearly number of international tourist arrivals spent in country c before arriving at an airport of region by air for each destination country. From the IATA data res r, we substitute parameter tc by htic if the person is a we calculate the total number of arrivals per year for each res returning resident, htic being the average number of days country and hence can infer the ratio of visitors to return- a returning resident spends in country c before returning ing residents. As we lack sufficient data, we assume that the home. If the person is a visitor, parameter tc is substituted ratio of visitors to residents is the same for each month. vis by htic , the average number of days a visitor spends in country c before arriving at an airport of region r. We distinguish between returning residents and visitors since Calculating the absolute number of infected pas- res vis sengers htic htic . We assume that the length of stay for returning residents Given the above, we can now determine the number of in- follows a normal distribution with mean equal to 15 days fected passengers I arriving at airport k during month res k,m and standard deviation of 2, i.e. htic ∼ N (15, 2). A pre- m as follows: vious study has shown that employees around the world are on average entitled to approximately 15 days of an- X res vis Ik,m = ωi,j(c, k) qpc,m + (1 − q)pc,m , (4) nual leave [52]. On the other hand, visitors likely spent i,j,c all their lives in the endemic country. We assume that where q is the proportion of residents inferred from the in- vis htic ∼ N (µvis, 0.1µvis), where µvis is equal to c’s me- ternational tourism arrival data,

 htires−(n−1) htires res (1 − βc,m) c − (1 − βc,m) c htic ≥ n − 1 res  pc,m = (5)  htires res 1 − (1 − βc,m) c htic < n − 1, and

 htivis−(n−1) htivis vis (1 − βc,m) c − (1 − βc,m) c htic ≥ n − 1 vis  pc,m = (6)  htivis vis 1 − (1 − βc,m) c htic < n − 1.

Evaluation of the models uncertainty Parameter Range

βc,m [0.000001, 0.000445] tc (days) [1, 29200] n (days) [5, 24] We performed a thousand runs of the model for each edge in the network, drawing the parameters from their respective Table 1: The model parameter ranges used in Sobol’s method. distributions, to calculate the mean and standard deviation of dengue-infected passengers. In addition, we have conducted a global sensitivity analysis to identify the model Results parameters with the greatest influence. We used Sobol’s method [55] with 100,000 samples to carry out the sensi- We run our model for two different years to explore the tivity analysis. The parameter ranges are shown in Ta- robustness of the proposed methodology. Specifically, the ble 1. The analysis was done with SALib [56], an open- analysis is conducted for 2011 and 2015. The results for source Python library. the year 2015 are presented in the main manuscript, while

4 Figure 1: Predicted dengue importations for August 2015. The map shows the output of our model for August 2015.The area of a node increases with the number of dengue cases imported through the corresponding airport. Airports that are predicted to not receive any infections are not shown on the map. Endemic countries are coloured dark grey. Countries that are non-endemic and where dengue vectors Aedes aegypti and/or Aedes albopictus are present are coloured in light grey. The blue circles correspond to the top ten airports identiﬁed in Fig 2. The map was created with the Python GeoPandas package and publicly available shapeﬁles from Natural Earth (http://www.naturalearthdata.com/). the results for 2011 are presented in the supplementary Texas, and Queensland, Australia. A full ranking of all air- material. Fig 1 shows the number of predicted imported ports located in non-endemic countries with vector presence dengue infections per airport for August 2015, where the can be found in Table S4 of the supplementary material. area of a node increases with the number of dengue cases im- 2015 ported through the corresponding airport. The map clearly 300 shows that many non-endemic regions where the dengue- MIA (Florida) LAX (California) transmitting vectors Aedes aegypti or Aedes albopictus are CDG (France) present (coloured in light grey) have airports that are pre- 250 MCO (Florida) SFO (California) dicted to receive a high number of dengue infections. For AMS (Netherlands) a list of dengue endemic and non-endemic countries see Ta- FLL (Florida) 200 ORY (France) ble S3. As resources for the control and prevention of dengue IAH (Texas) are often limited [57], these countries face a high risk of fu- FRA (Germany) ture endemicity. 150

In Fig 2 and Fig S2 we plot the number of predicted Estimated imported cases dengue importations over time for the ten airports that re- 100 ceive the highest number of cases, lie in non-endemic regions with vector presence and where local cases have been 50 reported in the past (more detailed plots with conﬁdence Jan Mar May Jul Sep Nov intervals are shown in Fig‘S3). While the majority of airports listed in Fig 2 and Fig S2 are predicted to receive Figure 2: Predicted monthly dengue importations by airport for 2015. The number of predicted imported dengue infections for the top between 50 and 150 cases each month, Miami International ten airports in non-endemic countries/states with vector presence for each Airport (MIA) is estimated to receive between 146 and 309 month in 2015. A break in a line indicates that the corresponding airport was not amongst the top ten during the respective month. Airports are cases each month during both years. With Orlando Inter- abbreviated using the corresponding IATA code. A full list of abbreviations national Airport (MCO) and Fort LauderdaleHollywood In- can be found in the supplementary material (see Table S1). ternational Airport (FLL) also represented amongst the airports with the highest number of imported cases, Florida In addition to calculating the number of imported dengue faces a high risk of local dengue outbreaks. Los Angeles In- infections per airport, the model further provides the num- ternational Airport (LAX) is predicted to receive the second ber of infected passengers travelling between any two air- highest number of imported cases. In 2011 its monthly pre- ports, thus revealing common importation routes. Table 2 dictions vary between 97 and 205 cases and in 2015 between and Table S5 list the routes that carry the highest number 113 and 253 cases. The remaining airports listed in Fig 2 of infected passengers whose ﬁnal destinations lie in non- and Fig S2 are located in France, Germany, the Netherlands, endemic countries with vector presence. Table S6 lists the

5 Florida 2015 France 2015 Italy 2015 200 700 350 175 600 300 150 500 250 125 400 200 100 300 150 75 200 100 50 100 50 25

Estimated imported cases 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Spain 2015 Switzerland 2015 Queensland 2015 120 100 100 100 80 80 80 60 60 60 40 40 40 20 20 20

Estimated imported cases 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Returning residents Visitors

Figure 3: Predicted dengue infections imported by returning residents and visitors in 2015. Here we show the results for non-endemic countries/states with vector presence with the highest number of predicted imported dengue cases in 2015. The bars are stacked to distinguish between returning residents (green) and visitors (blue). The blue solid line corresponds to the total number of imported cases. The error bars correspond to the model’s coefficient of variation (see Material and methods). The six countries were selected because they are predicted to receive the highest number of dengue importations, are non-endemic and dengue vectors are established. routes that carry the highest number of infected passengers gers is predicted during April. The routes with the highest whose final destinations lie in non-endemic countries irre- estimated number of dengue-infected passengers terminate spective of whether vectors are present. For example, the at airports in countries that are non-endemic and where route between Denpasar and Perth is ranked third in 2011 dengue-transmitting vectors are present. in Table S6, but it is not considered in the ranking shown in Table S5, as there are no vectors in Perth. Fig S4 shows a map of all importation routes into non-endemic countries Returning residents and visitors with vector presence. Next, we aggregate airports by country/state to predict the number of imported dengue infections on a coarser level. Orig. Dest. Pax Month For non-endemic countries that cover an area larger than 2 SJU (Puerto Rico) MCO (Florida) 51 Jul 5,000,000 km and where dengue vectors are present we ag- PTP (Guadeloupe) ORY (France) 37 Aug gregate airports by state. These countries are Russia, the FDF (Martinique) ORY (France) 34 Aug United States of America and Australia. The comparison SJU (Puerto Rico) FLL (Florida) 32 Jul between passenger volumes recorded by IATA and official TPE (Taiwan) LAX (California) 31 Aug airport statistics indicated that the IATA data for Russia GRU (Brazil) MIA (Florida) 29 Apr may be inaccurate, i.e. the difference in passenger num- DEL (India) KBL (Afghanistan) 27 Aug bers is larger than 15% (see Material and Methods). Hence, GDL (Mexico) LAX (California) 24 Aug we did not perform a state-level analysis for this country. CUN (Mexico) MIA (Florida) 24 Aug In Australia vectors are present only in Queensland [58]. CUN (Mexico) LAX (California) 22 Aug While vectors have been observed in more than 40 different US states, autochthonous cases have been reported only in Table 2: The ten routes with the highest predicted number of California, Florida, Hawaii and Texas [59]. dengue-infected passengers with final destinations in non-endemic Our model separately calculates the number of dengue- countries with vector presence. The table lists the direct routes with the highest predicted volume of dengue-infected passengers who continue infected people amongst returning residents and visitors and to travel to non-endemic regions with vector presence and where local out- hence we can identify which of these groups is more likely to breaks have been reported in the past. The last column records the month during which the highest number of infected passengers are predicted. import the disease into a given country or state. Fig 3 and Fig S5 show the results for six non-endemic countries/states In both years the highest predicted number of infected with vector presence that are predicted to receive the high- passengers are recorded during the northern hemisphere’s est number of dengue importations each month. Results summer. The route between SãoPaulo International Air- for the remaining countries and states are shown in Figs S6 port (GRU) and Miami International Airport (MIA) is the - S11. We observe that the contributions of returning resi- exception, where the highest number of infected passen- dents and visitors to the total number of imported dengue

6 Florida 2015 30 Brazil - 15.36% Puerto Rico - 13.33% 25 The Bahamas - 7.38%

Mexico - 6.89% 20 % Colombia - 6.25% Dominican Republic - 6.15% 15 Jamaica - 5.09% Haiti - 3.54% 10 Trinidad and Tobago - 3.08% Venezuela - 3.04% 5 Jan Mar May Jul Sep Nov Italy 2015 Brazil - 14.36% India - 13.61% Thailand - 6.89%

Mexico - 4.65% 17.5 Philippines - 4.28% 15.0 % Dominican Republic - 4.25% 12.5 Indonesia - 4.09% Egypt - 3.59% 10.0 Cuba - 3.45% 7.5 Singapore - 3.34% 5.0 Jan Mar May Jul Sep Nov Spain 2015 Brazil - 11.41% Colombia - 9.04% Dominican Republic - 8.95% 17.5

Mexico - 8.43% India - 5.16% 15.0 % Cuba - 4.06% 12.5 Venezuela - 3.65% 10.0 Argentina - 3.58% Ecuador - 3.44% 7.5 Philippines - 3.39% 5.0 Jan Mar May Jul Sep Nov

Figure 4: Predicted percentage contribution of dengue importations by country of acquisition in 2015. The predicted percentage contribution by source country and month in 2015. The size and colour of the circles indicate the percentage contribution of the corresponding country to the total number of imported cases. The y-labels indicate the yearly percentage contribution of the corresponding source country. infections is predicted to vary greatly between the different Caribbean and Latin America, with infections acquired in countries and states. In Florida and Queensland return- Puerto Rico (PRI) predicted to peak during June and July ing residents are predicted to be the main source of dengue and infections acquired in Brazil predicted to peak between importation. In France and Italy approximately one third January and April. We hypothesise that Florida receives of all dengue infections are predicted to be imported by such a high number of imported dengue cases due to its close visitors while in Spain visitors import around 75% of all proximity to the Caribbean, which has been endemic since imported cases. For Switzerland we do not have any infor- the 1970s [61]. France is predicted to receive many infec- mation about the ratio of returning residents to visitors. For tions from the Caribbean, in particular from Martinique and the United States there is evidence in the form of surveil- Guadeloupe which are French overseas regions and hence a lance reports that returning residents are indeed the main high volume of air traffic from these regions to metropoli- contributors to dengue importations [60]. For Queensland tan France is expected. These predictions align with the we predict that 95% and 94% of infections were imported fact that outbreaks of dengue in France coincide with out- by returning residents in 2011 and 2015, respectively. Our breaks in the French West Indies, where most reported cases predictions are supported by Queensland’s dengue notifica- are acquired [62, 63]. In Italy the model predicts that the tion data (provided by Queensland Health), showing that most common countries of acquisition are India and Brazil. 97% and 92% of all dengue importations in 2011 and 2015, India and Brazil are also the most common countries of ac- respectively, were imported by returning residents. quisition for Switzerland in 2011. In 2015 Switzerland is predicted to receive most of their dengue importations from India and Thailand. Spain is predicted to import the major- Countries of acquisition ity of infections from Latin America and the Caribbean. For In addition to being able to distinguish between returning Queensland the model predicts that imported cases are ac- residents and visitors, the model also divides the imported quired mostly in South-East Asia with Indonesia being the cases according to their places of acquisition. Fig 4 and largest source. This is in agreement with previous stud- Fig S12 show the model’s estimated percentage contribution ies [64] and the dengue case data that was provided by of dengue importations by source country. Queensland Health. In addition, we performed a rank-based Florida is predicted to import most infections from the validation of these results.

7 A B 2015 2015 FijiFiji Taiwan Indonesia 20 Somalia Maldives 18 Nauru 80 Nicaragua 16 Sri Lanka Brazil 14 Cambodia 60 Myanmar 12 Solomon Islands TiTimor-Lestemor-Leste 10 Samoa 40 Vietnam 8 Tonga Thailand India Reported ranking 6 Malaysia Reported importations 20 Philippines Papua New Guinea Papua New Guinea 4 Philippines Malaysia India Thailand 2 Indonesia 0 TaiwanFiji 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 0 25 50 75 100 125 150 Predicted ranking Predicted importations

Figure 5: Rank-based validation and correlation between reported and predicted imported cases for Queensland in 2015. (A) Countries are ranked by the total number of predicted and reported imported dengue cases. The reported ranking is then plotted against the predicted ranking. Countries that were ranked by the model, but did not appear in the dataset receive a rank of i + 1, were i is the number of unique importation sources according to the dengue case data. Similarly, countries that appeared in the data and were not ranked by the model receive a rank of i + 1. For circles that lie on the x = y line (grey solid line) the predicted and reported rankings are equal. Circles that lie between the two dashed lines correspond to countries with a difference in ranking that is less than or equal to five. The circle areas are scaled proportionally to the number of reported cases that were imported from the corresponding country. Spearman’s rank correlation coefficient between the absolute numbers of reported and predicted importations is equal to 0.6. (B) The absolute number of reported dengue importations are plotted against the absolute number of predicted importations.

We obtained dengue case data from Queensland Health, round in Taiwan [26] and approximately 44,000 and 16,000 which records the places of acquisition for each dengue case Queensland residents travelled to Taiwan in 2011 and 2015, reported in Queensland. We rank the countries of acquisi- respectively. tion by the total number of predicted and reported dengue- Some of the differences between the observed percentages infected people who arrive in Queensland. We then plot the and the predicted percentages can be explained by under- reported ranking against the predicted ranking. In addi- reporting. It is possible that dengue awareness among trav- tion, we plot the absolute number of reported importations ellers to one country is greater than the awareness amongst against the absolute number of predicted importations and travellers to another country. Travellers with higher aware- calculate Spearman’s rank correlation coefficient. Fig 5 and ness levels are more likely to report to a doctor if feeling Fig S13 show the results. unwell after their return. The rank-based validation of our model demonstrates that overall, the model captures the different importation sources Country-specific reporting rates well. It does particularly well for the countries from which Queensland receives the most infections. Spearman’s rank The reporting rate of a disease is defined as the ratio of correlation coefficient is equal to 0.6 for the year 2015 and reported infections to actual infections. Dengue reporting equal to 0.58 for the year 2011. Below we explain some of rates vary greatly across space and time and are difficult to the differences between the data and the model output. determine [10]. The usual approach to estimating country- For the rank-based validation the two largest outliers in specific reporting rates is to carry out cohort or capture- both years are Fiji and Taiwan. The predicted ranking for recapture studies that can be costly, are time consuming Fiji in 2011 is 2, while the reported ranking is 10. In 2015 and may be biased [28]. we estimate Fiji to be ranked fifth, however no cases were We utilised our model to infer country- and state-specific reported in 2015 and hence Fiji is ranked last amongst the reporting rates of imported cases by performing a least reported cases. According to the Fijian government tourists squares linear regression without intercept. are less likely to contract the disease than local residents as Table 3 and Table S7 show the estimated yearly and they tend to stay in areas that are not infested by Aedes seasonal reporting rates of imported cases for Queens- aegypti mosquitoes [65] or where there is likely considerable land, Florida, France, Italy and Spain. To distinguish control effort undertaken by tourism accommodation opera- locally acquired and imported cases in Queensland, we tors. Since the incidence rates incorporated into our model use case-based data from Queensland Health where do not distinguish between different regions of a source coun- the country of acquisition is recorded. Travel-related try, the model is unable to account for such nuances. In dengue cases reported in Europe are published by the 2011 and 2015 we estimate Taiwan to be ranked seventh European Centre for Disease Prevention and Control and eighth, respectively, however no cases were reported in (http://ghdx.healthdata.org/gbd-results-tool). both years. This result is surprising as dengue occurs year- Data for Florida is available from the Florida De-

8 Dec-Feb Mar-May Jun-Aug Sep-Nov Yearly Queensland 32.4 48.9 18.6 22.6 28.6 Spain 14 14 31.7 26.3 23.5 Italy 4.5 6.8 9.2 13.1 9 France 3.8 6.9 9.7 7.1 7.2 Florida 0.9 0.7 1.2 2.7 1.4

Table 3: Yearly and seasonal reporting rates of imported cases in 2015. The table shows the estimated reporting rates of imported cases for Queensland, Spain, Italy, France and Florida. We estimate the reporting rates by using a least squares linear regression without intercept.

partment of Health (http://www.floridahealth.gov/ between parameters tc and n with a second-order index of diseases-and-conditions/mosquito-borne-diseases/ 0.07. surveillance.html). The results show that estimated reporting rates of imported cases are highest in Queensland, in particular during Discussion autumn. This is expected as dengue awareness campaigns are intensified between November and April [66]. In con- To mitigate the risk of outbreaks from importation of trast, Florida has the lowest dengue reporting rate (1.3% in dengue into non-endemic regions it is critical to predict the 2011 and 1.4% in 2015). This finding is supported by a pre- arrival time and location of infected individuals. We mod- vious study which found that awareness levels in Florida are elled the number of dengue infections arriving each month extremely low [67]. The estimated reporting rates for the at any given airport, which enabled us to estimate the num- European countries are also low; however, the model pre- ber of infections that are imported into different countries dicts a substantial increase from 2011 to 2015. The question and states each month. In addition, the model determines why reporting rates in Queensland are higher is challenging the countries of acquisition and hence is able to uncover the to answer, as we do not have any information about the routes along which dengue is most likely imported. Our re- true number of imported cases. However, Queensland has sults can also be used to estimate country- and state-specific one of the best dengue prevention programs in the world. reporting rates of imported cases. According to Queensland Health, other states and countries Such knowledge can inform surveillance, education and frequently ask for training and advice regarding surveillance risk mitigation campaigns to better target travellers along and awareness campaigns. high risk importation routes at the most appropriate times. It will also help authorities to more efficiently surveil those Model uncertainty airports with the highest risk of receiving dengue-infected passengers. We found that the average coefficient of variation of our The model proposed here overcomes many of the short- importation model is 19.5% across both years. That is, the comings of previous models, however, it is not without limi- model’s standard deviation is on average equal to 19.5% of tations. Validation through comparison of reported cases to its mean. Fig S14 shows the distribution of the coefficient predicted cases is infeasible due to the high degree of under- of variation for several destinations. reporting. However, we demonstrate that the coefficient of The results from the global sensitivity analysis show that variation of the model with 19.5% on average is low (see Ma- tc is the most important of the three model parameters with terial and Methods). A rank-based validation for Queens- a total-order index of 0.94 (see Fig S15). The different values land confirmed that the different importation sources are of the first-order and total-order indices indicate interaction accurately predicted. between the model parameters. The second-order indices Incidence rates may vary considerably from region to re- show that there is significant interaction between parame- gion within the same country [65] and higher resolution data ters tc and βc,m with a second-order index of 0.19, as well could improve the model’s predictions, as it would better as between parameters tc and n with a second-order index reflect the export of dengue cases from the individual re- of 0.1. gions. Region-specific incidence rates can, for instance, be Since the range of parameter tc is large ([1, 29200] days), combined with spatial patterns of the visiting frequency of we performed the sensitivity analysis again for a shorter travellers to determine the likelihood of travellers to export range of values ([1, 30] days) that is more realistic for re- dengue out of endemic countries. Additional data on indi- turning residents who spend their holidays in an endemic viduals’ travel behaviour may also be beneficial, as it can country. In this case, parameter βc,m, with a total-order be analysed to improve the estimation of the average time index of 0.6, is more important than tc, which has a total- that a person has spent in a specific country before arriving order index of 0.35 (see Fig S15). The second-order indices at a given airport. Our assumption that returning residents show that there is still significant interaction between pa- and visitors are exposed to the same daily incidence rates rameters tc and βc,m with a second-order index of 0.06, and is a simplification. Further details on the types of accom-

9 modation, for example, resorts vs local housing, could also trol at http://atlas.ecdc.europa.eu/public/index.aspx. be used to inform the daily incidence rates, due to varia- Case-based dengue notifications for Queensland cannot be tions in vector control. The global sensitivity analysis has shared as it contains confidential information. The authors revealed that tc, the number of days a traveller has spent in gained access to this data in accordance with Section 284 of country c, is the most important model parameter. Hence, the Public Health Act 2005. additional data on individuals’ travel behaviour may sub- stantially improve the model. Knowledge about the exact Acknowledgments age of visitors who reside in non-endemic countries would also improve the model. Currently, we assume that the age We would like to thank Frank de Hoog and Simon Dunstall of a visitor is equal to the median age of the population of for their constructive feedback which helped us to improve the country in which the visitor resides. In reality, the age the model. We would also like to thank Queensland Health of air passengers may differ from the median age, especially for providing dengue outbreak data. This work is part of for developing countries. the DiNeMo project. In temperate regions local conditions may not allow for dengue to be transmitted during the winter months. Thus, even a large number of imported cases during those months References would not trigger local outbreaks. Variable seasonality pat- [1] David E. Bloom, Steven Black, and Rino Rappuoli. terns due to El NiñoSouthern Oscillation can affect the Emerging infectious diseases: A proactive approach. spread of dengue in tropical and subtropical regions. An Proc. Natl. Acad. Sci., 114(16):4055–4059, 2017. interesting direction for future research is to combine the here proposed model with knowledge of local conditions and [2] Dirk Brockmann and Dirk Helbing. The hidden geom- weather phenomena like El NiñoSouthern Oscillation to etry of complex, network-driven contagion phenomena. evaluate the risk of local outbreaks. In this work we studied Science, 342(6164):1337–1342, 2013. dengue importation via air travel. In future, we will also consider other modes of transportation to develop a more [3] Ilaria Dorigatti, Arran Hamlet, Ricardo Aguas, comprehensive model. Lorenzo Cattarino, Anne Cori, Christl A Donnelly, Tini Garske, Natsuko Imai, and Neil M Ferguson. Inter- national risk of yellow fever spread from the ongoing Data availability statement outbreak in Brazil, December 2016 to May 2017. Eu- rosurveillance, 22(28):30572, 2017. The air travel data used in this study are owned by a third party and were licensed for use under contract by Inter- [4] R. Guimera, S. Mossa, A. Turtschi, and L. A. N. national Air Travel Association (IATA)- Passenger Intelli- Amaral. The worldwide air transportation network: gence Services (PaxIS): http://www.iata.org/services/ Anomalous centrality, community structure, and cities’ statistics/intelligence/paxis/Pages/index.aspx. global roles. Proc. Natl. Acad. Sci., 102(22):7794–7799, The same data can be purchased for use by any other 2005. researcher by contacting: Phil GENNAOUI Regional [5] Zhuojie Huang and Andrew J Tatem. Global malaria Manager - Aviation Solutions (Asia Pacific) Tel: +65 connectivity through air travel. Malar. J., 12(1):269, 6499 2314 — Mob: +65 9827 0414 [email protected] — 2013. www.iata.org Monthly dengue incidence rates for all countries for the [6] L. Hufnagel, D. Brockmann, and T. Geisel. Forecast years 2011 and 2015 are available as supplementary infor- and control of epidemics in a globalized world. Proc. mation files. Natl. Acad. Sci., 101(42):15124–15129, 2004. Median population age data is publicly available from the Central Intelligence Agency at https: [7] A. J. Tatem, Z. Huang, A. Das, Q. Qi, J. Roth, and //www.cia.gov/library/publications/resources/ Y. Qiu. Air travel and vector-borne disease movement. the-world-factbook/fields/343.html. Parasitology, 139(14):1816–1830, 2012. International tourism arrival data used in this study [8] Isaac I Bogoch, Oliver J Brady, Moritz U G Krae- are owned by a third party and cannot be shared pub- mer, Matthew German, Marisa I Creatore, Manisha A licly. The data is available for purchase from the Kulkarni, John S Brownstein, Sumiko R Mekaru, Si- World Tourism Organisation at . . https://www eunwto org/ mon I Hay, Emily Groot, Alexander Watts, and Kam- . action/doSearch?ConceptID=2445&target=topic ran Khan. Anticipating the international spread of Zika Dengue notification data from Australia is publicly avail- virus from Brazil. Lancet, 387(10016):335–336, 2016. able from the Australian Department of Health at http: //www9.health.gov.au/cda/source/rpt 1 sel.cfm. [9] Samir Bhatt, Peter W. Gething, Oliver J. Brady, Dengue notification data from Europe is publicly available Jane P. Messina, Andrew W. Farlow, Catherine L. from the European Centre for Disease Prevention and Con- Moyes, John M. Drake, John S. Brownstein, Anne G.

10 Hoen, Osman Sankoh, Monica F. Myers, Dylan B. [19] A. Wilder-Smith, M. Quam, O. Sessions, J. Rocklov, George, Thomas Jaenisch, G. R. William Wint, J. Liu-Helmersson, L. Franco, and K. Khan. The 2012 Cameron P. Simmons, Thomas W. Scott, Jeremy J. dengue outbreak in Madeira: Exploring the origins. Eu- Farrar, and Simon I. Hay. The global distribution and rosurveillance, 19(8), 2014. burden of dengue. Nature, 496(7446):504–507, 2013. [20] Mikkel B. Quam, Kamran Khan, Jennifer Sears, Wei [10] Jeffrey D Stanaway, Donald S Shepard, Eduardo A Un- Hu, Joacim Rocklöv,and Annelies WilderSmith. Es- durraga, Yara A Halasa, Luc E Coffeng, Oliver J Brady, timating air travelassociated importations of dengue Simon I Hay, Neeraj Bedi, Isabela M Bensenor, Car- virus into Italy. J. Travel Med., 22(3):186–193, 2015. los A Castañeda-Orjuela,Ting-Wu Chuang, Kather- ine B Gibney, Ziad A Memish, Anwar Rafay, Kings- [21] Eduardo Massad, Marcos Amaku, Francisco An- ley N Ukwaja, Naohiro Yonemoto, and Christopher J L tonio Bezerra Coutinho, Claudio José Struchiner, Murray. The global burden of dengue: An analysis from Marcelo Nascimento Burattini, Kamran Khan, Jing the Global Burden of Disease Study 2013. Lancet In- Liu-Helmersson, Joacim Rocklöv,Moritz U. G. Krae- fect. Dis., 16(6):712–723, 2016. mer, and Annelies Wilder-Smith. Estimating the probability of dengue virus introduction and secondary au- [11] Natasha Evelyn Anne Murray, Mikkel Quam, and An- tochthonous cases in Europe. Sci. Rep., 8(1):4629, nelies Wilder-Smith. Epidemiology of dengue: Past, 2018. present and future prospects. Clin. Epidemiol., 5:299– 309, 2013. [22] Katherine Standish, Guillermina Kuan, William Avilés, Angel Balmaseda, and Eva Harris. High dengue case [12] World Health Organization. WHO heralds new phase capture rate in four years of a cohort study in Nicaragua in the fight against neglected tropical diseases, 2013. compared to national surveillance data. PLoS Negl. Available at: http://www.who.int/mediacentre/ Trop. Dis., 4(3):e633, 2010. news/releases/2013/ntds report 20130116/en/ [Accessed 25/10/18]. [23] M. Kakkar. Dengue fever is massively under-reported in India, hampering our response. BMJ, 345(17):e8574, [13] Lauren Gardner and Sahotra Sarkar. A global airport- 2012. based risk model for the spread of dengue infection via the air transport network. PLoS One, 8(8):e72129, [24] S. Vong, S. Goyet, S. Ly, C. Ngan, R. Huy, V. Duong, 2013. O. Wichmann, G. W. Letson, H. S. Margolis, and P. Buchy. Under-recognition and reporting of dengue [14] John S Mackenzie, Duane J Gubler, and Lyle R Pe- in Cambodia: A capturerecapture analysis of the Na- tersen. Emerging flaviviruses: The spread and resur- tional Dengue Surveillance System. Epidemiol. Infect., gence of Japanese encephalitis, West Nile and dengue 140(03):491–499, 2012. viruses. Nat. Med., 10(12):S98–S109, 2004. [25] T. Y. M. Wahyono, J. Nealon, S. Beucher, A. Prayitno, [15] Cameron P. Simmons, Jeremy J. Farrar, Nguyen van A. Moureau, S. Nawawi, H. Thabrany, and M. Nad- Vinh Chau, and Bridget Wills. Dengue. N. Engl. J. jib. Indonesian dengue burden estimates: Review Med., 366(15):1423–1432, 2012. of evidence by an expert panel. Epidemiol. Infect., 145(11):2324–2329, 2017. [16] Hsu P-S Chen C-D Lian I-B Chao D-Y Chang F-S, Tseng Y-T. Re-assess vector indices threshold as an [26] International Association for Medical Assistence to early warning tool for predicting dengue epidemic in a Travellers (IAMAT). International Association for dengue non-endemic country. PLOS Negl Trop Dis., Medical Assistence to Travellers, 2018. Available at: 9(9):e0004043, 2015. https://www.iamat.org/ [Accessed 6/11/18].

[17] Jan C. Semenza, Bertrand Sudre, Jennifer Min- [27] Global Burden of Disease Collaborative Net- iota, Massimiliano Rossi, Wei Hu, David Kossowsky, work. Global Burden of Disease Study 2016 Jonathan E. Suk, Wim Van Bortel, and Kamran Khan. (GBD 2016) Results, 2017. Available at: International dispersal of dengue through air travel: http://ghdx.healthdata.org/gbd-results-tool Importation risk for Europe. PLoS Negl. Trop. Dis., [Accessed 9/11/18]. 8(12):e3278, 2014. [28] Nguyen T. Toan, Stefania Rossi, Gabriella Prisco, [18] Lauren M. Gardner and Sahotra Sarkar. Risk of Nicola Nante, and Simonetta Viviani. Dengue epidemi- dengue spread from the Philippines through interna- ology in selected endemic countries: Factors inﬂuencing tional air travel. Transp. Res. Rec. J. Transp. Res. expansion factors as estimates of underreporting. Trop. Board, 2501:25–30, 2015. Med. Int. Heal., 20(7):840–863, 2015.

11 [29] Airline Network News and Analysis. Aviation [40] Zambia: Transport Data Portal. Air transport database, 2018. Available at: https://www.anna.aero/ statistics Zambia, 2016. Available at: http: databases/ [Accessed 1/12/18]. //zambiamtc.opendataforafrica.org/ZMATS2015/ air-transport-statistics-zambia?airports= [30] Civil Aviation Administration of China. 2015 Civil 1000000-kenneth-kaunda-international-airport Aviation Airport Throughput Ranking, 2016. Avail- [Accessed 1/12/18]. able at: http://www.caac.gov.cn/XXGK/XXGK/TJSJ/ 201603/t20160331 30105.html [Accessed 1/12/18]. [41] California Department of Transportation. 2105:2014 [31] Ministry of Land Infrastructure Transport and air passenger and air cargo traffic activity re- Tourism. Ministry of Land, Infrastructure, Trans- port, 2016. Available at: http://www.dot.ca.gov/ port and Tourism,, 2016. Available at: https: hq/planning/aeronaut/documents/statistics/ //web.archive.org/web/20161021205147/http: 15trafficgrowthrpt.pdf [Accessed 1/12/18]. //www.mlit.go.jp/common/001141840.pdf [Accessed 1/12/18]. [42] Airports Authoriy of India. Passengers, 2016. Available at: https://www.aai.aero/sites/default/ [32] Ministry of Transportation Republic of Indonesia. files/traffic-news/Mar2k15annex3.pdf [Accessed Air transport traffic, 2018. Available at: http:// 1/12/18]. hubud.dephub.go.id/?en/llu/index/filter:bulan,0 [Accessed 1/12/18]. [43] Associazione Italiana Gestori Aeroporti. Statistiche, 2016. Available at: http://www.assaeroporti.com/ [33] Airports Council International. North America airport statistiche/ [Accessed 1/12/18]. traffic annual reports, 2015. Available at: https: //airportscouncil.org/intelligence/north- [44] Office National des Aéroports. Passengers, 2017. american-airport-traffic-reports/north- Available at: http://www.onda.ma/en/I-am-a- america-airport-traffic-annual-reports/ [Ac- Professional/Companies/statistics/(offset)/30 cessed 1/12/18]. [Accessed 1/12/18]. [34] Directorate General of Civil Aviation - Kuwait. Statis- [45] Airports Company South Africa. Statistcs, 2018. tics, 2015. Available at: https://www.dgca.gov.kw/ Available at: http://www.airports.co.za/news/ en/civil-aviation/media-and-info/statistics statistics [Accessed 1/12/18]. [Accessed 1/12/18]. [35] EANA - NavegaciónAéreaArgentina. Statistical re- [46] Egyptian Holding Company for Airports and Air Nav- ports, 2016. Available at: https://www.eana.com.ar/ igation. Statistics, 2015. Available at: http:// estadisticas#node-150 [Accessed 1/12/18]. www.ehcaan.com/statistics.aspx [Accessed 1/12/18].

[36] Angkasa Pura II. Innovating beyond excellence - [47] Airports Council International. Passenger Summary, 2015 annual report, 2015. Available at: https: 2018. Available at: https://aci.aero/data-centre/ //cms.angkasapura2.co.id/NUWEB PUBLIC FILES/ annual-traffic-data/passengers/2015-final- angkasapura2/Annual 25 07 2016 09 04 23.pdf summary/ [Accessed 1/12/18]. [Accessed 1/12/18]. [48] Department of Home Affairs. Overseas Arrivals and De- [37] Civil Aviation Authority of the Philippines. partures, 2017. Available at: https://data.gov.au/ Passenger movement, 2015. Available at: dataset/overseas-arrivals-and-departures [Ac- https://data.gov.ph/dataset/civil-aviation- cessed 22/11/18]. authority-philippines-passenger-movement [Accessed 1/12/18]. [49] Miranda Chan and Michael A. Johansson. The in- [38] Instituto de Estad´ısticas de Puerto Rico. Carga cubation periods of dengue viruses. PLoS One, y passajeros aéreos y mar´ıtimos, 2015. Available 7(11):e50972, 2012. at: http://www.estadisticas.gobierno.pr/iepr/ Estadisticas/InventariodeEstad%C3%ADsticas/ [50] G. Chowell, P. Diaz-Dueñas,J.C. Miller, A. Alcazar- tabid/186/ctl/view detail/mid/775/report id/ Velazco, J.M. Hyman, P.W. Fenimore, and C. Castillo- 9485fbd8-efa5-4583-a8a4-a39c74eb846f/ Chavez. Estimation of the reproduction number of Default.aspx [Accessed 1/12/18]. dengue fever from spatial epidemic data. Math. Biosci., 208(2):571–589, 2007. [39] Malaysia Airports. Connecting you seamlessly to the world - Annual report 2015, 2015. Avail- [51] Duane J. Gubler and Gary G. Clark. Dengue/dengue able at: http://mahb.listedcompany.com/misc/ar/ hemorrhagic fever: The emergence of a global health ar2015.pdf [Accessed 1/12/18]. problem. Emerg. Infect. Dis., 1(2):55–57, 1995.

12 [52] McCann D Messenger JC, Lee S. Working time around [63] Guy La Ruche, Dominique Dejour-Salamanca, Pascale the world: Trends in working hours, laws, and policies Bernillon, Isabelle Leparc-Goffart, Martine Ledrans, in a global comparative perspective. 1st ed. London: Alexis Armengaud, Monique Debruyne, Gérard- Routledge, 2007. Antoine Denoyel, and SégolèneBrichler. Capturere- capture method for estimating annual incidence of im- [53] Central Intelligence Agency. The World Fact- ported dengue, France, 2007–2010. Emerg. Infect. Dis., book, 2017. Available at: https://www.cia.gov/ 19(11):1740–1748, 2013. library/publications/the-world-factbook/ fields/2177.html{#}aq [Accessed 12/11/18]. [64] David Warrilow, Judith A. Northill, and Alyssa T. Pyke. Sources of dengue viruses imported into Queens- [54] World Tourism Organisation. All Countries: Inbound land, Australia, 2002–2010. Emerg. Infect. Dis., Tourism: Arrivals by mode of transport 1995 - 2017, 18(11):1850–1857, 2012. 2018. Available at: https://www.e-unwto.org/doi/ abs/10.5555/unwtotfb0000271519952017201809 [65] The Fijian Government. Minimal risk of dengue [Accessed 12/11/18]. fever in major tourism areas of Fiji, 2014. Available at: http://www.fiji.gov.fj/Media-Center/Press- [55] Sobol IM. Global sensitivity indices for nonlinear math- Releases/MINIMAL-RISK-OF-DENGUE-FEVER-IN- ematical models and their Monte Carlo estimates. Math MAJOR-TOURISM-AREA.aspx [Accessed 8/6/18]. Comput Simulat., 55:271–280, 2001. [56] Usher W Herman J. SALib: An open-source Python [66] Queensland Health. Queensland dengue man- library for sensitivity analysis. The Journal of Open agement plan 2015–2020, 2015. Available at: Source Software, 2(9):97, 2017. https://www.health.qld.gov.au/ data/assets/ pdf file/0022/444433/dengue-mgt-plan.pdf [Ac- [57] Amy C Morrison, Emily Zielinski-Gutierrez, cessed 29/10/18]. Thomas W Scott, and Ronald Rosenberg. Defin- ing challenges and proposing solutions for control of [67] Mary H. Hayden, Jamie L. Cavanaugh, Christo- the virus vector Aedes aegypti. PLoS Med., 5(3):e68, pher Tittel, Melinda Butterworth, Steven Haenchen, 2008. Katherine Dickinson, Andrew J. Monaghan, and Kacey C. Ernst. Post outbreak review: Dengue pre- [58] Nigel W. Beebe, Robert D. Cooper, Pipi Mottram, and paredness and response in Key West, Florida. Am. J. Anthony W. Sweeney. Australia’s dengue risk driven by Trop. Med. Hyg., 93(2):397–400, 2015. human adaptation to climate change. PLoS Negl. Trop. Dis., 3(5):e429, 2009. [68] Centers for Disease Control and Preven- tion. Dengue map, 2019. Available at: [59] Micah B. Hahn, Rebecca J. Eisen, Lars Eisen, Karen A. https://www.healthmap.org/dengue/en/ [Accessed Boegler, Chester G. Moore, Janet McAllister, Harry M. 31/07/19]. Savage, and John-Paul Mutebi. Reported Distribution of Aedes (Stegomyia) aegypti and Aedes (Stegomyia) albopictus in the United States, 1995-2016 (Diptera: Culicidae). J. Med. Entomol., 53(5):1169–1175, 2016. [60] Caitlin A.M. Van Dodewaard and Stephanie L. Richards. Trends in dengue cases imported into the United States from Pan America 2001–2012. Environ. Health Insights, 9:33–40, 2015. [61] Amarakoon, Dharmaratne, Anthony Chen, Sam Rawl- ins, Dave D. Chadee, Michael Taylor, and Roxann Sten- nett. Dengue epidemics in the Caribbean–temperature indices to gauge the potential for onset of dengue. Mitig. Adapt. Strateg. Glob. Chang., 13(4):341–357, 2008. [62] Victor Vasquez, Elie Haddad, Alice Perignon, Stéphane Jaureguiberry, Ségolène Brichler, Isabelle Leparc- Goffart, and Eric Caumes. Dengue, chikungunya, and Zika virus infections imported to Paris between 2009 and 2016: Characteristics and correlation with outbreaks in the French overseas territories of Guadeloupe and Martinique. Int. J. Infect. Dis., 72:34–39, 2018.

13 Supporting information

Table S1: List of airport abbreviations

IATA Name City (Country/State) IATA Name City (Country/State) 3-Letter 3-Letter Code Code AEP Jorge Newbery Airport Buenos Aires (Ar- LAX Los Angeles Interna- Los Angeles (California) gentina) tional Airport BKK Suvarnabhumi Airport Bangkok (Thailand) LHR Heathrow Airport London (UK) BNE Brisbane Airport Brisbane (Queensland) MAD Adolfo Suárez Madrid- Madrid (Spain) Barajas Airport BOM Chhatrapati Shivaji In- Mumbai (India) MCO Orlando International Orlando (Florida) ternational Airport Airport CDG Charles de Gaulle Air- Paris (France) MEX Mexico City Interna- Mexico City (Mexico) port tional Airport COK Cochin International Kochi (India) MIA Miami International Air- Miami (Florida) Airport port CUN Cancún International Cancún(Mexico) MNL Ninoy Aquino Interna- Manila (Philippines) Airport tional Airport DEL Indira Gandhi Interna- New Delhi (India) MTY Monterrey International Apodaca (Mexico) tional Airport Airport DFW Dallas/Fort Worth In- Dallas (Texas) MXP Milan Malpensa Airport Milan (Italy) ternational Airport DPS Ngurah Rai Interna- Denpasar (Indonesia) NRT Narita International Tokyo (Japan) tional Airport Airport DXB Dubai International Air- Dubai (UAE) ORY Paris Orly Airport Paris (France) port EZE Ministro Pistarini Inter- Buenos Aires (Ar- PER Perth Airport Perth (Western Aus- national Airport gentina) tralia) FDF Martinique Aimé Forte-de-France (Mar- PTP Pointe-à-Pitre Interna- Pointe-à-Pitre (Guade- Césaire International tinique) tional Airport loupe) Airport FLL Fort LauderdaleHol- Miami (Florida) PUJ Punta Cana Interna- Punta Cana (Dominican lywood International tional Airport Republic) Airport GDL Miguel Hidalgo y Cos- Guadalajara (Mexico) SAL Monseñor Oscar´ Arnulfo San Salvador (El Sal- tilla Guadalajara Inter- Romero International vador) national Airport Airport GRU SãoPaulo International SãoPaulo (Brazil) SDQ Las Américas Interna- Punta Caucedo (Do- Airport tional Airport minican Republic) ICN Incheon International Seoul (South Korea) SFO San Francisco Interna- San Francisco (Califor- Airport tional Airport nia) IAH George Bush Interconti- Houston (Texas) SJU Luis MuñozMar´ınInter- San Juan (Puerto Rico) nental Airport national Airport JFK John F. Kennedy Inter- New York City (New STI Cibao International Air- Santiago de los Ca- national Airport York) port balleros (Dominican Republic) KBL Hamid Karzai Interna- Kabul (Afghanistan) TPE Taiwan Taoyuan Inter- Taipei (Taiwan) tional Airport national Airport

14 Table S2: List of non-endemic countries where IATA data is inaccurate

Algeria Bahrain Bonaire, Saint Eustatius & Saba Bulgaria Central African Republic Croatia Egypt Federated States of Micronesia Finland Germany Guinea-Bissau Greece Hungary Iceland Iran Israel Malawi Morocco Netherlands Russian Federation Serbia Slovenia South Africa South Korea Tanzania Togo The Gambia Tunisia Turkey Uganda Ukraine Zambia

Table S3: List of countries indicating whether dengue vectors are present and whether the country is endemic. Information about endemicity was obtained from [68]. Information about vector presence was obtained from [26].

Country Endemic Vector Country Endemic Vector Country Endemic Vector presence presence presence Afghanistan no yes Ghana no yes Pakistan yes yes Albania no yes Gibraltar no yes Palau yes yes Algeria no yes Greece no yes Palestine no yes American no yes Greenland no no Panama yes yes Samoa Andorra no no Grenada yes yes Papua New yes yes Guinea Angola yes yes Guadeloupe yes yes Paraguay yes yes Anguilla yes yes Guam no no Peru yes yes Antarctica no no Guatemala yes yes Philippines yes yes Antigua and yes yes Guinea yes yes Poland no no Barbuda Argentina yes yes Guinea-Bissau no yes Portugal no yes Armenia no yes Guyana yes yes Puerto Rico yes yes Aruba yes yes Haiti yes yes Qatar no no Australia no yes Honduras yes yes Reunion yes yes Austria no yes Hong Kong yes yes Romania no yes Azerbaijan no no Hungary no yes Russian Federa- no yes tion Bahrain no no Iceland no no Rwanda no yes Bangladesh yes yes India yes yes Saint Helena no no Barbados yes yes Indonesia yes yes Saint Kitts and yes yes Nevis Belarus no no Inner Hebrides no no Saint Lucia yes yes Belgium no yes Iran no no Saint Pierre and no no Miquelon Belize yes yes Iraq no no Saint Vin- yes yes cent and the Grenadines Benin no yes Ireland no no Samoa no yes Bermuda no yes Israel no yes Sao Tome and no no Principe Bhutan yes yes Italy no yes Saudi Arabia yes yes Bolivia yes yes Jamaica yes yes Senegal yes yes Bonaire, Saint no yes Japan no no Serbia no yes Eustatius & Saba Bosnia and no yes Jordan no yes Seychelles yes yes Herzegovina Botswana no no Kazakhstan no no Sierra Leone yes yes Brazil yes yes Kenya yes yes Singapore yes yes Brunei yes yes Kiribati no yes Sint Maarten no yes Bulgaria no yes Kuwait no no Slovakia no yes Burkina Faso yes yes Kyrgyzstan no no Slovenia no yes Burundi no yes Laos yes yes Solomon Islands yes yes Cambodia yes yes Latvia no no Somalia yes yes Cameroon yes yes Lebanon no yes South Africa no no Canada no no Lesotho no no South Korea no no Cape Verde yes yes Liberia no yes South Sudan yes yes Cayman Islands yes yes Libya no no Spain no yes Central African no yes Liechtenstein no no Sri Lanka yes yes Republic Chad no yes Lithuania no no Sudan yes yes Channel Islands no no Luxembourg no no Suriname yes yes Chile no no Macau yes yes Swaziland no no China yes yes Macedonia no yes Sweden no no Christmas no no Madagascar yes yes Switzerland no yes Island Cocos (Keeling) no no Malawi no yes Syria no yes Islands Colombia yes yes Malaysia yes yes Taiwan yes yes Comoros yes yes Maldives no yes Tajikistan no no

15 Country Endemic Vector Country Endemic Vector Country Endemic Vector presence presence presence Congo no yes Mali yes yes Tanzania no yes Cook Islands no yes Malta no yes Thailand yes yes Costa Rica yes yes Marshall Islands no yes The Bahamas yes yes Cote d’Ivoire yes yes Martinique yes yes The Gambia no yes Croatia no yes Mauritania no yes Timor-Leste yes yes Cuba yes yes Mauritius yes yes Togo no yes Curacao no yes Mayotte yes yes Tonga no yes Cyprus no no Mexico yes yes Trinidad and yes yes Tobago Czech Republic no yes Moldova no no Tunisia no no Democratic yes yes Monaco no yes Turkey no yes Republic of the Congo Denmark no no Mongolia no no Turkmenistan no no Djibouti yes yes Montenegro no yes Turks and yes yes Caicos Islands Dominica yes yes Montserrat yes yes Tuvalu no yes Dominican Re- yes yes Morocco no no Uganda no yes public Ecuador yes yes Mozambique yes yes Ukraine no no Egypt no yes Myanmar yes yes United Arab yes yes Emirates El Salvador yes yes Namibia no yes United King- no no dom Equatorial yes yes Nauru no yes United States no yes Guinea Eritrea yes yes Nepal yes yes United States no no Minor Outlying Islands Estonia no no Netherlands no yes Uruguay no no Ethiopia yes yes New Caledonia yes yes Uzbekistan no no Falkland Islands no no New Zealand no no Vanuatu yes yes Federated no yes Nicaragua yes yes Venezuela yes yes States of Mi- cronesia Fiji no yes Niger no yes Vietnam yes yes Finland no no Nigeria yes yes Virgin Islands yes yes France no yes Niue no yes Wallis and Fu- no yes tuna Islands French Guiana yes yes Norfolk Island no no Western Sahara no no French Polyne- no yes North Korea no no Yemen yes yes sia Gabon yes yes Northern Mari- no yes Zambia no yes ana Islands Georgia no yes Norway no no Zimbabwe no yes Germany no yes Oman yes yes

16 Table S4: Annual estimated imported dengue cases per airport

Code Imported Imported Name City Country/State cases 2011 cases 2015 MIA 2413 2547 Miami International Miami US/Florida LAX 1518 1871 Los Angeles Intl Los Angeles US/California CDG 941 1227 Charles De Gaulle Paris-De Gaulle France/Île-de- France SFO 831 1166 San Francisco Intl San Francisco US/California MCO 822 1036 Orlando Intl Orlando US/Florida FLL 792 970 Ft Lauderdale Intl Fort Lauderdale US/Florida ORY 652 788 Orly Paris-Orly France/Île-de- France IAH 599 810 George Bush Intercontinental Houston- US/Texas Intercontinental EZE 586 648 Ministro Pistarini Buenos Aires Argentina/Autonomous City of Buenos Aires MAD 385 439 Adolfo Suarez-Barajas Madrid Spain/Community of Madrid DFW 381 478 Dallas/Ft Worth Intl Dallas/Fort Worth US/Texas BNE 379 529 Brisbane Intl Brisbane Australia/Queensland MXP 356 408 Malpensa Milan-Malpensa Italy/Lombardy FCO 343 424 Fiumicino Rome-Da Vinci Italy/Lazio AEP 258 225 Jorge Newbery Buenos Aires-Newbery Argentina/Autonomous City of Buenos Aires MLE 204 214 Ibrahim Nasir International Male Maldives/Malé POS 198 150 Piarco International Port of Spain Trinidad and Tobago/Port of Spain TPA 160 224 Tampa International Tampa US/Florida SXM 159 184 Prinses Juliana International St. Maarten Sint Maarten BCN 148 207 Barcelona Barcelona Spain/Catalonia CUR 147 173 Hato International Curacao Curacao SAN 142 181 San Diego International Airport San Diego US/California HNL 123 153 Honolulu Intl Honolulu/Oahu US/Hawaii BEY 122 162 Rafic Hariri International Beirut Lebanon/Beirut KBL 109 155 Kabul International Kabul Afghanistan/Kabul ACC 97 126 Kotoka International Accra Ghana/Greater Accra SJC 88 99 San Jose Municipal San Jose US/California SAT 80 127 San Antonio Intl San Antonio US/Texas VCE 75 108 Marco Polo Venice Italy/Veneto AUS 71 123 Austin-Bergstrom International Airport Austin US/Texas SMF 70 94 Sacramento International Sacramento US/California OAK 65 65 Metro Oakland Intl Oakland US/California LYS 56 72 Satolas Lyon France/Auvergne- Rhône-Alpes OOL 55 126 Coolangatta Gold Coast Australia/Queensland JAX 53 74 Jacksonville Intl Jacksonville US/Florida MRS 53 69 Marignane Marseille France/Provence- Alpes-Côte d’Azur NCE 53 71 Cote D’Azur Nice France/Provence- Alpes-Côte d’Azur BLQ 49 59 Guglielmo Marconi Bologna Italy/Emilia- Romagna COR 46 78 Pajas Blancas Córdoba Argentina/Córdoba TLS 42 53 Blagnac Toulouse France/Occitanie COO 39 66 Cadjehoun Cotonou Benin/Littoral ONT 39 43 Ontario Intl Ontario US/California SAH 38 11 Sana’a International Sana’a Yemen/Sana’a LIN 38 56 Linate Milan-Linate Italy/Lombardy FAT 37 42 Fresno Yosemite International Fresno US/California SNA 37 58 John Wayne Airport Orange County US/California DLA 33 60 Douala International Douala Cameroon/Littoral KGL 29 48 Kigali International Airport Kigali Rwanda/Kigali PNS 27 31 Pensacola International Pensacola US/Florida BOD 24 33 Merignac Bordeaux France/Nouvelle- Aquitaine CAY 24 38 Felix Eboue Cayenne France/French Guiana NAN 23 27 Nadi International Nadi Fiji/Ba PBM 22 34 Johan A. Pengel Intl Paramaribo Suriname/Paramaribo CNS 22 37 Cairns International Cairns Australia/Queensland ELP 22 25 El Paso Intl El Paso US/Texas NTE 21 23 Chateau Bougon Nantes France/Pays de la Loire FLR 21 26 Peretola Florence Italy/Tuscany BUR 18 9 Hollywood-Burbank Burbank US/California HOU 18 38 William P Hobby Houston-Hobby US/Texas

17 Code Imported Imported Name City Country/State cases 2011 cases 2015 PPG 17 18 Pago Pago Intl Pago Pago American Samoa/Maoputasi County TRN 17 20 Citta Di Torino Turin Italy/Piedmont ROB 17 17 Roberts Intl Monrovia-Roberts Liberia MFE 15 14 Miller International McAllen US/Texas PBI 15 23 Palm Beach Intl West Palm Beach US/Florida LGB 15 13 Long Beach Municipal Long Beach US/California BZV 15 29 Maya Maya Brazzaville Congo/Brazzaville NAP 14 16 Capodichino Naples Italy/Campania TLH 14 21 Tallahassee International Tallahassee US/Florida MDZ 13 20 El Plumerillo Mendoza Argentina/Mendoza ROS 13 25 Islas Malvinas Rosario Argentina/Santa Fe CRP 13 15 Corpus Christi Intl Corpus Christi US/Texas RSW 13 14 Southwest Florida International Fort Myers US/Florida PMI 13 15 Palma De Mallorca Palma de Mallorca Spain/Balearic Islands MPL 13 18 Mediterranee Montpellier France/Occitanie VPS 12 14 Destin-Ft Walton Beach Airport Destin-Ft Walton Beach US/Florida VRN 12 8 Verona Verona Italy/Veneto FGI 11 20 Fagali’I Apia Samoa/Tuamasaga GNV 11 16 J R Alison Regional Municipal Gainesville US/Florida OGG 11 13 Kahului Kahului/Maui US/Hawaii VLC 11 16 Valencia Airport Valencia Spain/Valencian Community CTA 11 11 Fontanarossa Catania Italy/Sicily BJM 10 17 Bujumbura Intl Bujumbura Burundi/Bujumbura Mairie TAB 10 8 ANR Robinson International Tobago Trinidad and Tobago AGP 10 15 Malaga Airport Malaga Spain/Andalusia ADE 10 3 Aden International Aden Yemen/Aden HRE 10 22 Harare International Harare Zimbabwe/Harare PNR 9 19 Pointe Noire Pointe Noire Congo PUF 9 10 Uzein Pau France/Nouvelle- Aquitaine BIO 9 15 Bilbao Airport Bilbao Spain/Basque Autonomous Community GOA 9 10 Cristoforo Colombo Genoa Italy/Liguria LPA 9 14 Gran Canaria Gran Canaria Spain/Canary Islands GRK 9 11 Regional/R.Gray AAF Killeen/Fort Hood US/Texas WDH 9 10 Windhoek Intl Windhoek Namibia/Khomas MAF 9 13 Midland-Odessa Regl Midland/Odessa US/Texas TRW 9 11 Bonriki International Tarawa Kiribati TSV 9 12 Townsville International Townsville Australia/Queensland PSP 9 11 Palm Springs Muni Palm Springs US/California MLH 9 10 Euroairport Mulhouse/Basel France/Grand Est BES 8 11 Bretagne Brest France/Brittany NKC 8 13 Nouakchott Nouakchott Mauritania/Nouakchott BRC 8 12 San Carlos Bariloche International San Carlos Bariloche Argentina/R´ıo Negro LBB 8 10 Preston Smith Intl Lubbock US/Texas AMA 8 10 Rick Husband Intl Amarillo US/Texas EYW 7 12 Key West Intl Key West US/Florida NDJ 7 16 Ndjamena N’Djamena Chad/N’Djamena DAL 7 22 Dallas Love Field Dallas-Love US/Texas ECP 5 11 Northwest Florida Beaches International Panama City US/Florida Airport NIM 5 12 Diori Hamani International Airport Niamey Niger/Niamey SPN 3 11 Saipan International Saipan Northern Mari- ana Islands SFB 0 10 Sanford International Orlando-Sanford US/Florida

18 Table S5: The ten routes with the highest predicted number of dengue-infected passengers with ﬁnal destinations in non-endemic countries with vector presence.

Orig. Dest. Pax Month SJU (Puerto Rico) MCO (Florida) 52 Jul FDF (Martinique) ORY (France) 34 Aug CUN (Mexico) MIA (Florida) 32 Aug SDQ (Dominican Republic) MIA (Florida) 30 Aug CCS (Venezuela) MIA (Florida) 28 Aug GDL (Mexico) LAX (California) 27 Aug SJU (Puerto Rico) FLL (Florida) 25 Jul PUJ (Dominican Republic) MIA (Florida) 24 Jul MNL (Philippines) LAX (California) 23 Jul SJU (Puerto Rico) MIA (Florida) 23 Jul

Table S6: The ten routes with the highest predicted number of dengue-infected passengers who continue to travel to non-endemic regions. The table lists the direct routes with the highest predicted volume of dengue-infected passengers who continue to travel to non-endemic regions irrespective of vector presence. The last column records the month during which the highest number of infected passengers are predicted.

2011 2015 Origin Destination Pax Month Origin Destination Pax Month BOM DXB 108 Jul BOM DXB 142 Aug CUN MEX 86 Aug DEL DXB 97 Aug DPS PER 77 Jan CUN MEX 75 Aug SDQ JFK 76 Aug COK DXB 72 Aug STI JFK 76 Aug DPS PER 65 Jan DEL DXB 72 Jul MAA DXB 59 Aug MNL ICN 71 Aug MNL ICN 95 Aug DEL LHR 65 Aug HYD DXB 55 Aug MNL NRT 65 Jul SJU JFK 57 Aug MTY MEX 62 Sep DEL LHR 59 Aug

Table S7: Yearly and seasonal reporting rates of imported cases in 2011.

Dec-Feb Mar-May Jun-Aug Sep-Nov Yearly Queensland 38.4 25.2 13.7 18.9 24.3 Italy 5.7 4 1.9 7.3 4.4 France 2.2 3.1 4.8 1.3 3 Florida 1.2 0.5 1 2.5 1.3

19 Onset Individual gets date bitten with Day of Day of probability ßc,m recovery return

time

time spent in country c (tc)

Figure S1: Illustration of the possibility of recovery before return. If an individual gets infected with dengue while overseas, but recovers before returning to region r, the individual cannot infect other people in region r.

2011 MIA (Florida) 300 LAX (California) CDG (France) AMS (Netherlands) 250 FLL (Florida) MCO (Florida) ORY (France) SFO (California) 200 IAH (Texas) FRA (Germany) DFW (Texas) 150 BNE (Queensland) Estimated imported cases

100

Jan Mar May Jul Sep Nov

Figure S2: Predicted monthly dengue importations by airport for 2011. The number of predicted imported dengue infections for the top ten airports in non-endemic countries/states with vector presence for each month in 2011. A break in a line indicates that the corresponding airport was not amongst the top ten during the respective month. Airports are abbreviated using the corresponding IATA code. A full list of abbreviations can be found in the supplementary material (see Table S1)

20 A MIA 2011 LAX 2011 CDG 2011 MCO 2011 SFO 2011 AMS 2011 160 250 140 140 350 140 225 140 120 120 300 200 120 120

175 100 100 100 250 100

150 80 80 80 200 80 125 Estimated imported cases 60 60 60 150 100 60

40 40 40 75 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov FLL 2011 ORY 2011 IAH 2011 FRA 2011 DFW 2011 BNE 2011 100

70 45 90 120 70 70

80 60 40

100 60 60 70 50 35

60 80 30 50 40 50 50 25 Estimated imported cases 60 30 40 40 40 20 20 40 30 30 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov B MIA 2015 LAX 2015 CDG 2015 MCO 2015 SFO 2015 AMS 2015 300 200 350 180 160 160 275 180

250 160 140 300 160 140 225 140 120 140 120 250 200 120 175 120 100 100 100 200 150 100 80 80 Estimated imported cases 125 80 150 80 60 60 100 60

Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov FLL 2015 ORY 2015 IAH 2015 FRA 2015 DFW 2015 BNE 2015 110 90 60 140 90 100 120 80 55

120 90 80 70 50 100 80 60 45 100 70 80 70 50 40 60 80 35 60 40 Estimated imported cases 60 30 50 50 30 60 40 20 25 40 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Figure S3: Predicted monthly dengue importations by airport The number of predicted imported dengue infections for the top ten airports in non-endemic countries/states with vector presence for each month in (A) 2011 and (B) 2015. The error bars correspond to ±1 standard deviation. Airports are abbreviated using the corresponding IATA code.

21 Figure S4: Dengue-infected passengers who continue to travel to non-endemic countries/states with vector presence for every route in the air transportation network This map corresponds to August 2015. The thickness as well as the colour of an edge represent the number of infected people travelling along the corresponding route. Blue represents relatively lower numbers of infected people, red represents relatively higher numbers of infected travellers and yellow represents the mid range.

Florida 2011 France 2011 Italy 2011 700 250 600 140 500 200 120 100 400 150 80 300 100 60 200 40 50 100 20

Estimated imported cases 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Spain 2011 Switzerland 2011 Queensland 2011 100 20 100 60 80 50 15 80 60 40 60 10 30 40 40 5 20 20 20 10 Estimated imported cases 0 Estimated imported cases 0 Jan Mar May Jul Sep Nov 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Returning residents Visitors

Figure S5: Predicted dengue infections imported by returning residents and visitors in 2011 Here we show the results for non-endemic countries/states with vector presence with the highest number of predicted imported dengue cases in 2011. The bars are stacked to distinguish between returning residents (green) and visitors (blue). The blue solid line corresponds to the total number of imported cases. The error bars correspond to the model’s coeﬃcient of variation (see Material and methods).

22 Alabama 2011 Arizona 2011 Arkansas 2011 California 2011 Colorado 2011 Connecticut 2011 40 35 500 17.5 12 8 35 30 15.0 10 400 30 12.5 25 6 25 8 300 20 20 10.0 6 4 15 200 15 7.5 4 10 10 5.0 2 100 2 5 5 2.5

Estimated imported cases 0 0 0 0 0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Delaware 2011 District of Columbia 2011 Georgia US 2011 Hawaii 2011 Illinois 2011 Indiana 2011 100 140 20.0 0.0012 35 25 17.5 30 80 120 0.0010 20 15.0 25 100 0.0008 60 12.5 20 15 80 0.0006 10.0 60 15 40 10 7.5 0.0004 10 40 5.0 20 5 0.0002 5 20 2.5

Estimated imported cases 0.0000 0 0 0 0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Iowa 2011 Kansas 2011 Kentucky 2011 Louisiana 2011 Maryland 2011 Massachusetts 2011 45 100 7 40 4 20 25 6 35 80 20 5 3 15 30 60 4 15 25 20 3 2 10 10 15 40 2 10 1 5 5 20 1 5

Estimated imported cases 0 0 0 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Michigan 2011 Minnesota 2011 Mississippi 2011 Missouri 2011 Nebraska 2011 New Hampshire 2011 50 6 40 7 3.0 40 35 6 40 5 2.5 30 5 30 4 2.0 30 25 4 3 20 1.5 20 20 3 2 15 1.0 10 2 10 10 1 5 1 0.5

Estimated imported cases 0 0 0 0 0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov New Jersey 2011 New Mexico 2011 New York 2011 North Carolina 2011 Ohio 2011 Oklahoma 2011 160 6 600 80 40 10 140 5 70 35 120 500 60 30 8 100 4 400 50 25 6 80 3 300 40 20 60 4 2 200 30 15 40 20 10 1 2 20 100 10 5

Estimated imported cases 0 0 0 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Oregon 2011 Pennsylvania 2011 Rhode Island 2011 South Carolina 2011 Tennessee 2011 Texas 2011 6 20.0 100 16 25 17.5 5 14 200 80 15.0 12 20 4 150 12.5 60 10 15 10.0 3 8 100 7.5 40 2 6 10 5.0 4 20 1 5 50 2.5 2

Estimated imported cases 0.0 0 0 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Utah 2011 Virginia 2011 Washington 2011 West Virginia 2011 100 14 50 20 2.5 12 80 40 2.0 1510 60 8 30 1.5 10 6 40 20 1.0 54 20 10 0.5

Imported DENV cases 2

Estimated imported cases 0 0 0 0.0 Jan Mar MayMay JulJul SepSep NovNov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Returning residents Visitors

Figure S6: Predicted imported dengue infections for returning residents and visitors for US states in 2011. The bars are stacked to distinguish between returning residents (green) and visitors (blue). The blue solid line corresponds to the total number of imported cases. The error bars correspond to the model’s coeﬃcient of variation (13.49%) that was inferred through Monte Carlo simulations.

23 Alabama 2015 Arizona 2015 Arkansas 2015 California 2015 Colorado 2015 Connecticut 2015 40 14 10 25 35 600 50 12 30 8 500 20 10 40 25 400 8 6 30 15 20 6 300 15 4 20 10 200 4 10 2 10 5 2 5 100

Estimated imported cases 0 0 0 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Delaware 2015 District of Columbia 2015 Georgia US 2015 Hawaii 2015 Illinois 2015 Indiana 2015 30 40 175 0.05 80 35 25 150 20 30 0.04 60 20 125 25 15 100 0.03 20 15 40 75 10 0.02 15 10 10 50 0.01 20 5 5 5 25

Estimated imported cases 0.00 0 0 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Iowa 2015 Kansas 2015 Kentucky 2015 Louisiana 2015 Maryland 2015 Massachusetts 2015 30 35 5 120 8 25 30 40 4 25 100 6 20 30 3 20 80 15 15 20 60 4 2 10 10 40 2 10 1 5 5 20

Estimated imported cases 0 0 0 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Michigan 2015 Minnesota 2015 Mississippi 2015 Missouri 2015 Nebraska 2015 New Hampshire 2015 50 60 50 6 8 4.0 40 7 3.5 50 40 5 6 3.0 40 30 30 4 5 2.5 30 4 2.0 3 20 20 3 1.5 20 2 10 10 2 1.0 10 1 1 0.5

Estimated imported cases 0 0 0 0 0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov New Jersey 2015 New Mexico 2015 New York 2015 North Carolina 2015 Ohio 2015 Oklahoma 2015 80 160 8 700 50 12 70 140 600 60 40 10 120 6 500 50 8 100 400 30 80 4 40 6 300 60 30 20 4 40 200 20 2 10 20 100 10 2

Estimated imported cases 0 0 0 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Oregon 2015 Pennsylvania 2015 Rhode Island 2015 South Carolina 2015 Tennessee 2015 Texas 2015 30 100 10 17.5 30 300 25 80 15.0 8 25 250 20 12.5 200 60 6 20 15 10.0 15 150 40 4 7.5 10 5.0 10 100 20 2 5 2.5 5 50

Estimated imported cases 0 0 0 0.0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Utah 2015 Virginia 2015 Washington 2015 West Virginia 2015 120 20 70 2.5 20 100 60 15 2.0 15 80 50 40 1.5 10 60 10 30 40 1.0 5 20 5 20 0.5

Imported DENV cases 10

Estimated imported cases 0 0 0 0.0 Jan Mar MayMay JulJul SepSep NovNov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Returning residents Visitors

Figure S7: Predicted imported dengue infections for returning residents and visitors for US states in 2015. The bars are stacked to distinguish between returning residents (green) and visitors (blue). The blue solid line corresponds to the total number of imported cases. The error bars correspond to the model’s coeﬃcient of variation (13.49%) that was inferred through Monte Carlo simulations.

24 A ACT 2011 NSW 2011 NT 2011 SA 2011 120 14 2.0 20 100 12 10 1.5 80 15 8 60 1.0 10 6 40 4 0.5 5 20 2

Estimated imported cases 0.0 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov TAS 2011 VIC 2011 WA 2011 3.5 140 100 3.0 120 80 2.5 100 2.0 60 80 1.5 60 40 1.0 40 20 0.5 20

Estimated imported cases 0.0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov B ACT 2015 NSW 2015 NT 2015 SA 2015 200 16 35 2.5 175 14 30 150 2.0 12 25 125 10 1.5 20 100 8 15 1.0 75 6 50 4 10 0.5 25 2 5

Estimated imported cases 0.0 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov TAS 2015 VIC 2015 WA 2015 175 5 175 20 150 4 150 125 15 125 3 100 100 10 2 75 75 50 50 5 1 25 25 Imported DENV cases

0Estimated imported cases 0 30 0 0 JanJan MarMarMayMay JulJulSepSepNovNov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Returning residents Visitors

Figure S8: Predicted imported dengue infections for returning residents and visitors for Australian states. ACT: Australian Capital Territory, NSW: New South Wales, NT: Northern Territory, SA: South Australia, TAS: Tasmania, VIC: Victoria, WA: Western Australia. The bars are stacked to distinguish between returning residents (green) and visitors (blue). The blue solid line corresponds to the total number of imported cases. The error bars correspond to the model’s coeﬃcient of variation (13.49%) that was inferred through Monte Carlo simulations.

25 Albania 2011 Armenia 2011 Austria 2011 Azerbaijan 2011 Belarus 2011 Belgium 2011 0.8 0.14 1.0 25 1.0 0.7 50 0.12 0.8 20 0.6 0.10 0.8 40 0.5 0.6 15 0.08 0.6 0.4 30 0.06 0.4 10 0.4 0.3 20 0.04 0.2 0.2 5 0.2 10 0.02 0.1

Estimated imported cases 0.00 0.0 0 0.0 0.0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Bosnia and Herzegovina 2011 Bulgaria 2011 Croatia 2011 Cyprus 2011 Czech Republic 2011 Denmark 2011 1.75 40 1.2 3.5 14 0.12 35 1.50 12 0.10 1.0 3.0 30 1.25 2.5 10 0.08 0.8 25 1.00 2.0 8 20 0.06 0.6 0.75 1.5 6 15 0.04 0.4 0.50 1.0 4 10 0.02 0.2 0.25 0.5 2 5

Estimated imported cases 0.00 0.0 0.00 0.0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov England 2011 Estonia 2011 Finland 2011 Georgia 2011 Germany 2011 Greece 2011 8 160 14 500 0.6 0.5 7 140 12 400 0.5 6 0.4 120 10 0.4 5 100 300 0.3 8 0.3 4 80 6 200 3 0.2 60 0.2 2 40 4 100 0.1 0.1 1 20 2

Estimated imported cases 0 0.0 0 0.0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Hungary 2011 Iceland 2011 Ireland 2011 Kazakhstan 2011 Kyrgyzstan 2011 Latvia 2011 5 4.0 0.8 17.5 0.5 3.5 0.7 0.5 15.0 4 0.4 0.6 3.0 12.5 0.4 2.5 0.5 3 0.3 10.0 0.3 2.0 0.4 7.5 2 1.5 0.3 0.2 0.2 1.0 0.2 5.0 1 0.1 0.1 0.5 0.1 2.5

Estimated imported cases 0.0 0.0 0.0 0 0.0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Lithuania 2011 Luxembourg 2011 Macedonia 2011 Malta 2011 Moldova 2011 Montenegro 2011 0.25 0.6 0.30 1.6 0.16 0.200 0.20 0.5 0.175 0.25 1.4 0.14 1.2 0.12 0.150 0.20 0.15 0.4 1.0 0.10 0.125 0.15 0.8 0.3 0.100 0.10 0.08 0.10 0.6 0.2 0.06 0.075 0.4 0.05 0.04 0.050 0.05 0.1 0.2 0.02 0.025

Estimated imported cases 0.00 0.0 0.00 0.0 0.00 0.000 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Netherlands 2011 Northern Ireland 2011 Norway 2011 Poland 2011 Portugal 2011 Romania 2011 140 7 50 2.5 30 3.0 6 120 40 2.0 25 2.5 100 5 20 2.0 80 1.5 4 30 15 3 1.5 60 1.0 20 40 10 2 1.0 0.5 10 20 5 1 0.5

Estimated imported cases 0 0.0 0 0 0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Russian Federation 2011 Scotland 2011 Serbia 2011 Slovakia 2011 Slovenia 2011 Sweden 2011 0.08 20.0 0.40 60 25 17.5 1.0 0.07 0.35 50 0.06 15.0 0.8 0.30 20 40 12.5 0.05 0.25 0.6 0.04 15 30 10.0 0.20 7.5 0.4 0.03 0.15 10 20 5.0 0.02 0.10 0.2 5 10 2.5 0.01 0.05

Estimated imported cases 0 0.0 0.0 0.00 0.00 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Turkey 2011 Ukraine 2011 Wales 2011 0.7 30 8 0.6 2025 7 6 0.5 20 15 5 0.4 15 4 10 0.3 3 10 0.2 5 2 5 1 0.1 Imported DENV cases Estimated imported cases 0 0 0.0 Jan MarMar MayMay JulJul SepSep NovNov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Returning residents Visitors

Figure S9: Predicted imported dengue infections for returning residents and visitors for European countries in 2011. The bars are stacked to distinguish between returning residents (green) and visitors (blue). The blue solid line corresponds to the total number of imported cases. The error bars correspond to the model’s coeﬃcient of variation (13.49%) that was inferred through Monte Carlo simulations.

26 Albania 2015 Armenia 2015 Austria 2015 Azerbaijan 2015 Belarus 2015 Belgium 2015 1.4 70 1.4 40 2.00 0.4 1.2 1.2 35 1.75 60 30 1.0 0.3 1.0 1.50 50 25 0.8 0.8 1.25 40 0.2 20 1.00 0.6 0.6 30 15 0.75 0.4 20 0.1 0.4 10 0.50 0.2 5 0.25 0.2 10

Estimated imported cases 0.0 0.0 0 0.00 0.0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Bosnia and Herzegovina 2015 Bulgaria 2015 Croatia 2015 Cyprus 2015 Czech Republic 2015 Denmark 2015 25 1.4 3.5 50 0.8 4 3.0 1.2 20 2.5 40 0.6 1.0 3 15 0.8 2.0 30 0.4 2 1.5 0.6 10 20 0.4 1.0 0.2 1 5 0.2 0.5 10

Estimated imported cases 0.0 0.0 0 0.0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov England 2015 Estonia 2015 Finland 2015 Georgia 2015 Germany 2015 Greece 2015 700 250 2.00 14 16 600 1.75 12 2.0 200 14 500 1.50 10 12 1.5 150 400 1.25 8 10 1.00 8 300 6 1.0 100 0.75 6 200 4 0.50 0.5 50 4 100 0.25 2 2

Estimated imported cases 0 0.00 0 0.0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Hungary 2015 Iceland 2015 Ireland 2015 Kazakhstan 2015 Kyrgyzstan 2015 Latvia 2015 1.4 35 3.5 1.0 5 1.2 30 8 3.0 0.8 4 1.0 25 2.5 6 0.8 2.0 0.6 3 20 0.6 15 4 1.5 0.4 2 0.4 10 1.0 2 0.2 1 0.2 5 0.5

Estimated imported cases 0 0.0 0 0 0.0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Lithuania 2015 Luxembourg 2015 Macedonia 2015 Malta 2015 Moldova 2015 Montenegro 2015 3.5 1.6 1.0 1.2 0.35 1.4 3.0 0.4 0.30 0.8 1.0 1.2 2.5 0.25 1.0 0.8 0.3 2.0 0.6 0.20 0.8 0.6 1.5 0.2 0.15 0.6 0.4 1.0 0.4 0.10 0.4 0.2 0.1 0.2 0.5 0.2 0.05 Estimated imported cases Estimated imported cases 0.0 0.0 0.0 0.0 0.0 0.00 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Netherlands 2015 Northern Ireland 2015 Norway 2015 Poland 2015 Portugal 2015 Romania 2015 50 14 7 175 60 2.5 12 6 150 40 50 2.0 10 5 125 40 30 8 4 100 1.5 30 75 20 6 3 1.0 20 50 4 2 10 25 0.5 2 10 1 Estimated imported cases Estimated imported cases 0 0.0 0 0 0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Russian Federation 2015 Scotland 2015 Serbia 2015 Slovakia 2015 Slovenia 2015 Sweden 2015 30 2.5 1.0 100 1.6 25 1.4 40 80 2.0 0.8 1.2 20 30 60 1.5 1.0 0.6 15 0.8 1.0 0.4 20 40 10 0.6 0.4 20 5 0.5 0.2 10 0.2

Estimated imported cases 0 0 0.0 0.0 0.0 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Turkey 2015 Ukraine 2015 Wales 2015 12 0.6 50 20 10 0.5 40 15 8 0.4 30 6 0.3 10 20 4 0.2 5 10 2 0.1 Imported DENV cases

Estimated imported cases 00 0 0.0 JanJan MarMar MayMay JulJul SepSepNovNov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Returning residents Visitors

Figure S10: Predicted imported dengue infections for returning residents and visitors for European countries in 2015. The bars are stacked to distinguish between returning residents (green) and visitors (blue). The blue solid line corresponds to the total number of imported cases. The error bars correspond to the model’s coeﬃcient of variation (13.49%) that was inferred through Monte Carlo simulations.

27 A Algeria 2011 Benin 2011 Botswana 2011 Burundi 2011 Cameroon 2011 Central African Republic 2011 6 6 2.00 1.6 5 1.4 5 1.75 1.4 5 1.2 1.50 4 4 1.2 1.0 4 1.25 1.0 3 0.8 3 3 1.00 0.8 0.6 0.75 2 2 2 0.6 0.50 0.4 0.4 1 1 1 0.25 0.2 0.2

Estimated imported cases imported Estimated 0 0 0.00 0.0 0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Chad 2011 Congo 2011 Egypt 2011 Ghana 2011 Guinea-Bissau 2011 Lesotho 2011 1.2 3.0 40 12 0.8 0.08 35 1.0 2.5 10 0.7 0.07 30 0.6 0.06 0.8 2.0 8 25 0.5 0.05 0.6 1.5 20 6 0.4 0.04 15 0.4 1.0 4 0.3 0.03 10 0.2 0.02 0.2 0.5 5 2 0.1 0.01

Estimated imported cases imported Estimated 0.0 0.0 0 0 0.0 0.00 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Liberia 2011 Libya 2011 Malawi 2011 Mauritania 2011 Morocco 2011 Namibia 2011 2.5 5 1.75 7 1.2 1.2 1.50 6 2.0 4 1.0 1.0 1.25 5 0.8 0.8 1.5 3 1.00 4 0.6 0.6 1.0 2 0.75 3 0.50 0.4 2 0.4 0.5 1 0.25 0.2 1 0.2

Estimated imported cases imported Estimated 0.0 0 0.00 0.0 0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Niger 2011 Rwanda 2011 Swaziland 2011 Tanzania 2011 Togo 2011 The Gambia 2011 0.8 0.12 14 2.5 0.7 4 2.5 0.10 12 0.6 2.0 2.0 0.5 3 0.08 10 8 1.5 0.4 0.06 1.5 2 0.3 6 0.04 1.0 1.0 0.2 4 1 0.5 0.5 0.1 0.02 2

Estimated imported cases imported Estimated 0.0 0 0.00 0 0.0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Tunisia 2011 Uganda 2011 Zambia 2011 Zimbabwe 2011 3.5 8 2.0 3.0 1.0 6 2.5 0.8 1.5 2.0 0.6 1.0 4 1.5 0.4 1.0 0.5 2 0.5 0.2

Estimated imported cases imported Estimated 0.0 0 0.0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov B Algeria 2015 Benin 2015 Botswana 2015 Burundi 2015 Cameroon 2015 Central African Republic 2015 2.5 8 2.00 1.0 8 5 7 1.75 2.0 6 1.50 0.8 4 6 5 1.5 1.25 0.6 3 4 1.00 1.0 4 2 3 0.75 0.4 2 0.50 2 1 0.5 0.2 1 0.25

Estimated imported cases imported Estimated 0 0 0.00 0.0 0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Chad 2015 Congo 2015 Egypt 2015 Ghana 2015 Guinea-Bissau 2015 Lesotho 2015 2.00 50 6 16 1.2 1.75 14 0.20 5 40 1.0 1.50 12 4 1.25 30 10 0.8 0.15 1.00 3 8 0.6 0.10 0.75 20 6 2 0.4 0.50 10 4 0.05 0.25 1 2 0.2

Estimated imported cases imported Estimated 0.00 0 0 0 0.0 0.00 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Liberia 2015 Libya 2015 Malawi 2015 Mauritania 2015 Morocco 2015 Namibia 2015 2.5 2.00 2.00 1.2 2.5 1.75 1.75 8 1.0 2.0 1.50 2.0 1.50 6 0.8 1.5 1.25 1.5 1.25 1.00 1.00 0.6 1.0 0.75 4 1.0 0.75 0.4 0.50 0.50 0.5 0.5 2 0.25 0.25 0.2

Estimated imported cases imported Estimated 0.0 0.00 0.0 0.00 0 0.0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Niger 2015 Rwanda 2015 Swaziland 2015 Tanzania 2015 Togo 2015 The Gambia 2015 0.16 1.6 17.5 2.00 6 0.14 3.0 1.4 15.0 1.75 0.12 1.2 5 12.5 2.5 1.50 1.0 0.10 4 10.0 2.0 1.25 0.8 0.08 1.00 3 7.5 1.5 0.6 0.06 0.75 2 5.0 1.0 0.4 0.04 0.50 0.2 1 0.02 2.5 0.5 0.25

Estimated imported cases imported Estimated 0.0 0 0.00 0.0 0.0 0.00 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Tunisia 2015 Uganda 2015 Zambia 2015 Zimbabwe 2015 3.0 12 7 204.0 3.5 10 6 2.5 3.0 15 8 5 2.0 2.5 4 1.5 102.0 6 3 1.5 4 1.0 1.05 2 0.5 0.5 2 1 Estimated imported cases imported Estimated Estimated imported cases imported Estimated 0.00 0 0 0.0 JanJan MarMar MayMay JulJul SepSepNovNov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Returning residents Visitors

Figure S11: Predicted imported dengue infections for returning residents and visitors for non-endemic African countries. The bars are stacked to distinguish between returning residents (green) and visitors (blue). The blue solid line corresponds to the total number of imported cases. The error bars correspond to the model’s coeﬃcient of variation (13.49%) that was inferred through Monte Carlo simulations.

28 Florida 2011 France 2011 20 Puerto Rico - 13.18% Martinique - 17.07% Brazil - 10.37% 18 Guadeloupe - 8.88% 25 Dominican Republic - 9.96% 16 Brazil - 7.98%

Jamaica - 8.94% Reunion - 7.9% 20 % 14 % Mexico - 7.91% 12 India - 7.87% The Bahamas - 6.87% Thailand - 4.0% 15 Colombia - 4.56% 10 Mauritius - 3.65% Venezuela - 4.5% 8 Dominican Republic - 3.16% 10 Cayman Islands - 3.0% 6 Indonesia - 2.83% Haiti - 2.81% Mexico - 2.47% 5 4 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Italy 2011 Switzerland 2011 India - 16.65% 20 India - 21.79% 18 Brazil - 14.9% 18 Brazil - 10.7% 16 Sri Lanka - 6.57% Thailand - 8.65%

Philippines - 5.85% 16 Sri Lanka - 7.6%

% Dominican Republic - 4.72% 14 % Dominican Republic - 5.94% 12 Thailand - 4.39% 12 Indonesia - 5.53% 10 Mexico - 4.09% Singapore - 4.24% 8 Egypt - 3.28% 10 Philippines - 3.94% Cuba - 2.81% 8 Maldives - 3.49% 6 Maldives - 2.57% 6 Egypt - 3.1% 4 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Spain 2011 Queensland 2011 40 Brazil - 13.17% 14 Indonesia - 24.22% Dominican Republic - 11.86% Fiji - 16.4% 35 Mexico - 10.3% 12 Malaysia - 13.99% 30

Venezuela - 8.39% Philippines - 10.22% % % 25 Colombia - 7.94% 10 Thailand - 8.77% India - 5.72% India - 8.09% 20 Cuba - 4.89% 8 Taiwan - 2.59% 15 Argentina - 3.58% Papua New Guinea - 2.5% 10 Peru - 2.98% 6 Sri Lanka - 2.13% Bolivia - 2.51% Vietnam - 1.31% 5 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Figure S12: Predicted percentage contribution of dengue importations by country of acquisition in 2011. The predicted percentage contribution by source country and month in 2011. The size and colour of the circles indicate the percentage contribution of the corresponding country to the total number of imported cases. The y-labels indicate the yearly percentage contribution of the corresponding source country.

29 A B 18 2011 2011 TaiwanTaiwan Indonesia 16 BangladeshBangladesh 40 CambodiaCambodia 14 New CaledoniaCaledoniaNew PakistanPakistan 12 PanamaPanama 30 FijiFiji 10 Timor-LesteTimor-Leste Thailand VietnamVietnam 20 8 Sri LankaLankaSri MalaysiaMalaysia 6 Reported ranking IndiaIndia

PhilippinesPhilippines Reported importations 10 Philippines 4 Papua New GuineaGuineaPapua India ThailandThailand Malaysia Fiji 2 IndonesiaIndonesia 0 0 0 20 40 60 80 100 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 Predicted importations Predicted ranking

Figure S13: Rank-based validation and correlation between reported and predicted imported cases for Queensland in 2011. (A) Countries are ranked by the total number of predicted and reported imported dengue cases. The reported ranking is then plotted against the predicted ranking. Countries that were ranked by the model, but did not appear in the dataset receive a rank of i + 1, were i is the number of unique importation sources according to the dengue case data. Similarly, countries that appeared in the data and were not ranked by the model receive a rank of i + 1. For circles that lie on the x = y line (grey solid line) the predicted and reported rankings are equal. Circles that lie between the two dashed lines correspond to countries with a difference in ranking that is less than or equal to five. The circle areas are scaled proportionally to the number of reported cases that were imported from the corresponding country. Spearman’s rank correlation coefficient between the absolute numbers of reported and predicted importations is equal to 0.58. (B) The absolute number of reported dengue importations are plotted against the absolute number of predicted importations.

30 A Florida 2011 France 2011 Italy 2011 25000 14000 17500 12000 20000 15000 10000 12500 15000 8000 10000 10000 6000 7500 Frequency 4000 5000 5000 2000 2500 0 0 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Coefficient of variation Coefficient of variation Coefficient of variation Argentina 2011 Spain 2011 Queensland 2011 7000 10000 4000 6000 3500 8000 5000 3000 4000 6000 2500 2000 3000 4000

Frequency 1500 2000 2000 1000 1000 500 0 0 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 Coefficient of variation 0.0 0.1 0.2 0.3 0.4 Coefficient of variation Coefficient of variation B Florida 2015 France 2015 Italy 2015 17500 12000 14000 15000 10000 12000 12500 8000 10000 10000 6000 8000 7500 6000

Frequency 4000 5000 4000 2500 2000 2000 0 0 0 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 Coefficient of variation Coefficient of variation Coefficient of variation Argentina 2015 Spain 2015 Queensland 2015 8000 5000 7000 10000 6000 8000 4000 5000 3000 4000 6000 3000 4000 2000 Frequency 2000 2000 1000 1000 0 0 0 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 Coefficient of variation Coefficient of variation Coefficient of variation

Figure S14: The distribution of the coeﬃcient of variation for several destinations. (A) Distributions for 2011. (B) Distributions for 2015.

31 A B 1.0 0.200 total-order first-order 0.175 0.8 0.150

0.6 0.125 0.100 0.4 0.075

Sensitivity indices 0.050 0.2

Second-order sensitivity indices 0.025

0.0 0.000 c,m tc n tc × c,m c,m ×n tc ×n Model parameters Model parameters C D 0.6 total-order 0.200 first-order 0.175 0.5 0.150

0.4 0.125

0.3 0.100 0.075 0.2 Sensitivity indices 0.050 0.1

Second-order sensitivity indices 0.025

0.0 0.000 c,m tc n tc × c,m c,m ×n tc ×n Model parameters Model parameters

Figure S15: Sobol’s sensitivity analysis of the model’s parameters. Parameter βc,m denotes the daily dengue incidence rate of country c during month m, parameter tc denotes the number of days a traveller who arrives at a given airport has spent in country c and parameter n denotes the sum of the intrinsic incubation period and the infectious period in humans. (A) The first-order and total-order indices for the parameter ranges as shown in Table 1 of the main manuscript. The indices indicate that tc is the most important model parameter. (B) The second-order indices for the parameter ranges as shown in Table 1 of the main manuscript. There is significant interactions between parameters tc and βc,m and between parameters tc and n.(C) The first-order and total-order indices for a shorter range of value ([1, 30] days) for parameter tc. In this case βc,m is the most important parameter. (D) The second-order indices for a shorter range of value ([1, 30] days) for parameter tc. There is still significant interaction between parameters tc and βc,m and between parameters tc and n.