Although the United States eliminated indigenous wild polioviruses (WPVs) decades ago,[1] various sources of possible reintroduction of live polioviruses (LPVs) remain.[2] Specifically, WPVs from countries that sustain their transmission,[3] circulating vaccine-derived polioviruses (cVDPVs) imported from countries that use oral poliovirus vaccine (OPV),[4] and (un)intentional introductions from laboratories or vaccine production sites present small but real risks.[2] Prior importations of LPVs into Amish communities in North America led to their recognition as a potential and identifiable linked network of undervaccinated individuals.[4, 5]

Dynamic models offer insights about possible outbreaks[6–8] and they can account for heterogeneity in the population.[8–10] For polio immunization overall, heterogeneity represents a complex and important consideration in the United States, because even with very high rates of coverage some people remain undervaccinated and they may cluster.[11] Individual-based (IB) models use individual level data (e.g., age, sex, health status), and an assumed network structure to characterize interactions between all individuals in the population.[12] Specification of the network structure depends on the nature of transmission of the pathogen and the specific population(s) considered. Many published large-scale IB models assume that individuals mix homogeneously at particular places or events.[13–15] IB models may also use a bipartite graph to track movements of people to specific locations based on individual activity schedules derived from census data, surveys, or other data sources.[8] IB models stochastically capture contacts between individuals at mixing site locations, which leads to a self-organizing and dynamic network based on movements. Some IB models also use data from a geographical information system to specify the network.[16, 17] Rahmandad et al. explored potential network structures for poliovirus transmission models and concluded that assumptions made about network structures and mixing significantly influence the results.[18] Following up on a prior study[11] and using insights from an expert review and synthesis of the literature[19, 20] and model calibration process,[21] we developed an IB model to explore the potential for transmission of LPVs in a study population based on our characterization of the North American Amish. We do not specify the type of LPV that would be introduced, although an introduction of WPV type 1 or a cVDPV of any serotype would represent the most likely potential candidates in the context of current global poliovirus epidemiology[22–24]

Developing an IB model for the study population requires characterization of the network structure as well as individual attributes and activities. Current estimates suggest that approximately 276,000 Amish people[25] live in approximately 2,000 church districts (i.e., districts) distributed across 30 U.S. states and Ontario, Canada (Figure 1).[25] Districts include approximately 30 families with approximately 135 people on average who attend church services together every other Sunday at a home in the district, send their children to the same school, and interact closely as a community. A large proportion of Amish districts further cluster in strongly interconnected settlements, the largest of which consists of 246 districts as of 2013,[25] although some districts remain much more isolated. The Amish share some common values, but they also differ to some degree in the level of conservatism (characterized as low [blue triangle], medium [green dot], and high [red square] in Figure 1), (Kraybill D.B., personal communication) with individuals from like-minded districts somewhat clustered geographically and preferentially interacting (e.g., by visiting similar church services in other districts on the Sundays between their own district church services). Households, sometimes consisting of multiple related families, serve as the core structure within the study population, with approximately 20–35 households in each Amish district.[25–28] As districts begin to grow much beyond the average size, their members will decide to split into two districts so as to not become too large according to tradition. Thus, while the number of families varies in each individual district, the distribution remains relatively consistent over time and growth of the population leads to increasing numbers of districts.

Our simulation of the 1993 Canadian LPV introduction, which we approximated by introducing a LPV with a relatively high R0 and paralysis-to-infection ratio for a WPV3 virus into a Amish district in Montana, did not result in any cases or inter-district transmission in any of the 1000 iterations, although the virus reached approximately half of the 135 district residents in approximately 50% of all runs (see Appendix A6). This result appears consistent with the actual Canadian experience of transmission observed within the community of introduction with limited circulation and no reported infections outside of the community.[4]

Table 2 summarizes key results for the different levels of assumed immunity (i.e., HIF and IPV). Overall, it takes an average of approximately 80–100 days from the time of introduction until the first case appears (if 3 or more appear), with higher values for higher IPV use, and 110–140 days on average until the second case (if any cases occur). These results provide some indication of the ability of increased use of IPV to lead to a delay of the detection of cases and transmission in a population (i.e., for HIF low compare IPV high to IPV low), while higher levels of population immunity and sufficient levels of IPV can prevent transmission (i.e., for HIF high compare IPV high to IPV low). Table 2 reveals that the duration and intensity of poliovirus circulation within the population depend on the immunity assumptions, but we anticipate relatively low transmission overall. At the lowest immunity settings, a poliovirus infection introduced into the study population leads to infection at some point during the simulation in 2% of the study population on average (i.e., approximately 5,000 people) reaching 3% of the districts (i.e. approximately 60 districts, mostly clustered in settlements), and resulting in 13 paralytic cases on average, with up to almost 200 cases in some iterations. Figure 2 (top left) shows that on the lowest immunity settings, approximately 75% of the simulations reach less than 2% of the population before the virus dies out, and poliovirus transmission would most likely not reach more than 10% of the study population, with only 38 of 1,000 runs in which the infection reaches between 12 and 24% of the study population. Figure 2 (top right) also shows estimated cases on the lowest immunity settings ranging between 0 and 200, with approximately 70% of the iterations ending up with fewer than 10 cases. At higher immunity settings, the fraction of people infected seldom exceeds 2% and the number of cases rarely exceeds 10 (Table 2, Figure 2).

Figure 3 shows the fraction of simulations in which each of the 2,007 districts became infected and shows that the relatively dense and central settlements in the states of Ohio and Pennsylvania become infected most often (up to 5% or 6% of all runs at the lowest level of assumed immunity), while the more remote settlements (e.g., Montana, Missouri) rarely become infected. This suggests that the proximity to and connectedness with other districts represent important determinants of the outbreak kinetics. The random selection of the source district implies low probability of introduction into relatively more isolated areas. Figure 4 further shows a clear correlation between district density in the area of the source district and the resulting outbreak size, although we see some exceptions to this generalization.

The time of introduction also represents an important factor because of the impact of the assumed seasonality in the transmission probability and the activity schedule, which both impact R₀. Figure 5 shows the results of the 12×100 runs with different starting months (with all else equal) and confirms that winter introductions typically result in much less transmission, although the virus may still survive through the winter and spread during the next summer. The individually plotted results in Figure 5 show substantial variation in the results due to the stochastic nature of contacts that transmit the virus.

Our results provide important insights about the dynamics of a potential LPV introduction into the North American Amish population. The level of historic immunity and acceptance of IPV represent important sources of uncertainty, which we varied in our analyses. Unlike the general US population, which continues to benefit from high levels of population immunity overall due to high rates of childhood immunization, many young Amish people may remain fully susceptible to polioviruses, and we anticipate that these individuals interact preferentially with one another (i.e., cluster socially). The number of expected cases depends on the time and place of the virus introduction. For example, introduction into dense communities will result in continued transmission and much higher case counts on average than an introduction into relatively more remote settlements. Introduction during spring or summer will generally lead to more transmission and more cases as seasonal effects increase the force of viral transmission.

The IB model yields numerous potential realizations of possible futures that collectively provide information about the overall types of behavior that we might expect, but each individual run differs and this suggests an important role of stochastic events in determining the exact transmission path that follows an introduction in a highly heterogeneous population. While transmission within a district may occur after an LPV introduction, stochastic contacts between distant friends or family can significantly influence the course of the overall outbreak. Large community gatherings such as weddings represent potentially large sources of inter-district transmission, which accelerate viral spread during the spring and may prolong a poliovirus outbreak into the late fall. Given the relative isolation of Amish communities from any clusters of under-vaccinated individuals in the general population, we do not anticipate that a poliovirus outbreak in the Amish communities might immediately spill over into the general population or vice versa. However, in either case, efforts to detect the outbreak and prevent its spread would represent a high priority. Although preventing spread within a district after virus detection may represent a challenge given the speed of transmission within a district, efforts to prevent spread between districts with any feasible measures may offer the best opportunity to contain an outbreak and limit its size.

We highlight several important limitations of our approach. First, our model relies on a large number of assumptions and the estimates depend on the quality of the data and the model inputs used. With regard to the activity patterns, we believe the basic activity schedules probably reasonably represent typical patterns, but we remain highly uncertain about the occasional inter-district movements, which determine the large scale transmission patterns. Specifically, the frequency, size, and time of weddings as well as the composition of their guests (i.e., from nearby vs. distant districts) substantially affect the timing, duration, and size of outbreaks. In addition, significant uncertainty exists about how polioviruses transmit in populations, and our estimates depend on highly uncertain values. We characterized the transmission probabilities based on estimated R₀ values in historic poliovirus outbreaks appropriate for North America,[11, 21, 32] but we remain uncertain about whether these differ for the Amish. The two most important parameters we identified include the basic transmission probability throughout the year and the modifiers for activities with close or community contact, especially the activities that involve inter-district contact. In addition, the model assumes that all individuals go through the same relative infectiousness curve once infected. Our use of an average for all individuals rather than including variability between individuals may affect the behavior of the model (i.e., it inhibits some individuals from becoming relatively much better or worse individual spreaders), but we do not anticipate that this leads to any major impacts, and data to support an alternative characterization remain limited.[19] The model allows for a relatively high amount of preferential contact based on distance, mindset, gender, and age. However, we do not keep track of extended family and friendship structures within the study population (i.e., we only track the core family), which may reduce the extent of repeated mixing with individuals outside of the home district somewhat compared to reality (i.e., the model stochastically selects the destination for each distant visit from within a certain range and districts with a certain mindset).

Studies to assess the level of historic immunity and current immunization practices in Amish communities would significantly reduce the uncertainty around our estimates of possible numbers of cases. Although we believe our model captures the essential sources of inter-district transmission, additional quantitative insights into inter-district contact patterns among the Amish would also significantly improve the accuracy of our model, particularly regarding the preferential mixing aspects and the distribution of travel distances. Efforts to better map the levels of immunity in different Amish communities and connectedness between them may help to support any future efforts required to develop appropriate response strategies in the event of a possible future poliovirus introduction in these communities. The continued threat of LPV introduction leads to preparedness efforts, including recommendations for a United States IPV stockpile.[38] Even a single case of polio detected in the US, including in the Amish, would likely trigger an aggressive outbreak response. Efforts to remain prepared for outbreak response and plan a stockpile should consider the role of populations like the Amish and other sources of heterogeneity.[39]