Although the number of global polio cases has been declining over the past 15 years, as shown in Fig. 1, the proportion of polio as a result of importation is increasing, which is a major concern to polio eradication. The proportion has ranged from 0 to 62 % over the past 15 years, with the years 2005, 2010, and 2013 reporting the highest proportions. However, these numbers do not reflect importation events, but rather the overall polio cases in non-endemic polio countries as a result of importation from polio-endemic or polio-infected countries (Pakistan, Afghanistan, and Nigeria being the only endemic countries since 2010). These proportions hence cannot inform from where the importation originated and how many travelers imported polio. Here, we have developed a mathematical model to address this gap. Our model not only takes into account polio endemicity (force of infection), population size, polio vaccination coverage, and infectious period, but also the probability of a traveler being infectious at the time of travel. As both symptomatic and asymptomatic polio infections are known to transmit the virus, our model includes asymptomatic cases. As the ratio of asymptomatic to symptomatic polio is very high, most of our estimated importations of poliovirus are via asymptomatic travelers, and hence our estimated numbers of importation/exportation appear high. Our sensitivity analysis shows that the force of infection in the epidemic source country is the main driving factor for the importation risk, combined with the travel volume.

In the year 2014, out of nine polio-affected countries, we modeled that 665 polio infections (of which 662 were asymptomatic, and only 3 symptomatic) were exported globally. The majority of these poliovirus exportations originated from Pakistan (521 out of 665; 78.3 %). The number of polio exportations will vary from year to year. In 2013, for example, there were 462 estimated exportations of polio infections, and less than half can be attributed to Pakistan, with Somalia contributing almost the same amount as Pakistan, as there was a major polio outbreak in Somalia that year (Table 2). As per the sensitivity analysis, we found that for every 1 % variation in the force of infection there will be approximately 1 % variation in the time-dependent prevalence in the country.

About 600 potential poliovirus importations from nine polio-infected countries in one year into any country in the world present a sizable problem. However, our model cannot tell us how many of these importation events will lead to secondary cases or even outbreaks. It is the national coverage of polio immunization in a country that will determine its vulnerability for polio outbreaks after importation. The polio vaccination coverage rate in any given country together with the quality of its surveillance system and the speed of outbreak response will determine the magnitude of outbreaks following importation. Countries with high polio vaccination coverage rates may still see importations of polio cases (the majority of which will be asymptomatic and hence not detected), but are unlikely to see secondary cases. For example, countries such as Australia, New Zealand, the United States, and Singapore have reported importations, but given their high immunization coverage rates, no single secondary cases occurred [21, 22]. For Africa, Andre Mach et al. recently assessed the risk for polio outbreaks for 2013-2014, and the authors found 15 countries to be at high risk for WPV outbreaks, 5 at moderate-to-high risk, and 6 at low risk [23]. In 15 of the 33 African countries, less than half of the population resides in areas where surveillance performance indicators have met only minimum targets [23, 24].

Every year, the Hajj pilgrimage brings more than 2 million pilgrims from all over the world to Saudi Arabia, an event that is characterized by overcrowding [9]. Many of these pilgrims are from Nigeria, Pakistan, and Afghanistan - the three remaining polio-endemic countries - and other predominantly Moslem countries that are polio-infected. Hence, there has been long-standing concern about the potential introduction of polio into the Hajj with subsequent international spread. Our model estimated 20 importations of poliovirus into Saudi Arabia via Hajj pilgrims in the year 2013, and 21 in the year 2014. About 20 potential importations need to be taken seriously. Indeed, the Kingdom of Saudi Arabia has introduced mandatory polio vaccination at the point of entry for all pilgrims coming from polio-infected countries [9].

To prevent reintroduction of the poliovirus, in January 2014 India decided to tighten cross-border travel rules by introducing a new polio vaccine requirement for all travelers from polio-infected countries entering India [12, 25]. We previously estimated the number of travelers who would be affected by this new rule imposed by the Indian government to be approximately 233,800 travelers annually from the seven countries to India, and 346,800 Indian national residents to these seven countries, in the year 2013 [25]. Our model now adds more information: our findings estimate that 13 polio importations occurred in the year 2013, and 20 in 2014. In 2014, 100 % of these polio importations into India originated from Pakistan and Afghanistan, which is not surprising given that these two countries carry the main remaining burden of polio and have the highest travel volume to India. Although the travel volume from Pakistan to India was of the same order of magnitude as that for Afghanistan to India, the force of infection of polio was higher in Pakistan, and hence the probability of importing polio from Pakistan to India is higher compared to Afghanistan. Given the high asymptomatic-to-symptomatic ratio, most likely all 20 imported infections were asymptomatic. The total expected number of importations may seem low at first sight. However, one must consider that for the year 2014 this figure implies an incidence of 20 per 380,604 travelers (5 polio infections per 100,000 travelers), which is far from negligible. In other words, of the total number of 72,159 asymptomatic and symptomatic polio infections in the nine countries, 20 (about 0.027 %) of them were estimated to have traveled to India at the time of polio infection associated with viral shedding. The number of secondary cases will depend on the polio immunization coverage rate, which according to WHO was 70 % for India [20]. Fortunately, no single imported polio case was detected or officially reported in India in the years 2013 or 2014. We added an analysis of the preceding years (2010–2012) for comparison. The years 2010 and 2011 saw high numbers of importations mainly due to the much higher number of countries that reported at least one case of polio. As even one importation event can lead to substantial outbreaks associated with hundreds of million dollars spent for their control [3, 4], our finding of 20 importations in one year (2014) lends support to India’s strategy to protect its country from reinfection via travelers. India’s new vaccine policy would affect approximately 380,000 travelers, and approximately 19,000 vaccinations need to be administered per one averted poliovirus importation. Given the tragic consequences of re-infecting India with polio, the number of travelers that need to be vaccinated to avert poliovirus importation would be justified. India’s emphasis should be on preventing polio importation from Pakistan and Afghanistan.

Our model had the following limitations. For lack of data, we assumed that the probability of poliovirus infection is independent of the probability of travel; and for simplicity, we assumed that poliovirus infections are homogeneously distributed in polio-affected countries. These assumptions will lead to an overestimate of our results. For the estimation of outbound travel from polio-affected countries (scenario 1, Table 2), we obtained data from IATA. These data capture an estimated 90 % of all passengers traveling on commercial airlines worldwide, but do not incorporate land travel. Hence, they tend to underestimate international travel volumes between countries that share contiguous land borders (that is, where land-based border crossings are common). The true exportation numbers may therefore be even higher than we estimated, if ground travel volume is included. Unfortunately, data on ground travel volume is difficult to obtain for many of the polio-affected countries. However, India does publish the number of travelers into its country, and these data include air and land travel. As there are a lot of border crossings via land from Pakistan to India, it was important to include such land travel data for estimating poliovirus importation into India (scenario 3, Tables 4 and 5).