4.  Summary of publications reviewed
This section first describes the polio modeling-related papers from the three groups that support the GPEI according to the timing of their first publication: KRI (starting in 2003), IC (starting in 2006), and IDM (starting in 2014). As discussed in the next three sections, KRI, IC, and IDM each established primary collaborations with three of the GPEI partners, but all three groups benefited from access to GPEI data under a sharing agreement established in 2013 and all groups received financial and/or subject matter expertise support from multiple GPEI partners. Following the detailed discussion of this work, this section provides brief context about the other studies identified in the review that reported on poliovirus transmission modeling or economic analyses related to the polio endgame.

4.1.  KRI
Motivated by an interest in appropriately integrating economic, risk, decision, and dynamic disease models to demonstrate the difference between static and dynamic policy models and the importance of changes that occur over time, KRI polio modeling efforts began in 2001 [17] with retrospective characterization of the economic benefits of polio risk management in the United States [9]. Informal discussions of the preliminary work on this topic in late 2001 with the US Centers for Disease Control and Prevention (CDC) led to the establishment of a collaboration between KRI and CDC polio subject matter experts [17]. The KRI-CDC collaboration focused throughout the rest of the decade on the polio endgame (i.e. characterization of risks and risk management options for after WPV eradication). In 2003, KRI presented the decision options for post-WPV eradication policies [8] and developed a DEB dynamic transmission model for polio that included immunity states associated with WPV infection and vaccination with OPV and/or IPV, including transmission by individuals with asymptomatic infections [10]. Given the exclusive use of tOPV at that time, this transmission model used a generic poliovirus serotype and did not consider OPV evolution endogenously [10]. KRI focused on the global policy level and developed estimates of the costs for the different post-WPV-eradication decision options stratified by World Bank income levels (WBILs) to capture some important differences that exist between countries [11]. KRI also characterized the costs and value of the information from the global poliovirus laboratory network (GPLN), which supports global poliovirus surveillance [12]. KRI provided the first quantitative risk estimates for VAPP, cVDPVs, and iVDPVs [13]. The risk estimates appropriately varied by WBIL and type of poliovirus vaccine used by national immunization programs based on statistical analyses of available data at the time and as a function of different post-WPV eradication policies [13]. KRI used the transmission model [10] to explore post-WPV eradication outbreak response policies and provided key insights to the GPEI in 2005 [190] about the benefits of both pre- and post-WPV eradication outbreak response [14], which motivated investments in improvements in GPEI outbreak response activities. Many of these papers appeared in a 2006 special issue of Risk Analysis [15], which also included perspectives on risk management in a polio-free world [16] and on the history and nature of the collaborative modeling process used [17]. The retrospective economic analysis for the US showed significant (hundreds of billions of 2002 US dollars US$2002) in net benefits from US investments in polio immunization [9], which helped to strengthen US commitments to global polio eradication and risk management.
Following the development of the integrated model components (i.e. dynamic disease transmission, risk, decision, and economic), KRI performed an economic analysis of post-WPV eradication immunization policies [18]. Given the time horizons considered in the economic analyses that extended beyond the characterization of outbreak events, the integrated model included consideration of potential reinfection and asymptomatic participation in transmission of individuals with waned immunity, with paralysis only occurring in a small fraction of fully susceptible individuals. High-level policy discussions related to control vs. eradication in late 2006 motivated KRI to apply the post-eradication model to estimate the economics of eradication (followed by several different post-WPV eradication immunization policies) compared to a wide range of control options [19]. This analysis demonstrated that eradication (if technically and operationally feasible in a reasonable time) represented a better health and economic option than control with OPV in OPV-using countries [19]. Some discussions at the time included significant pessimism about the ability to stop poliovirus transmission in India and the other remaining endemic countries [191]. KRI modeling suggested that elimination could occur in India with sufficient immunization intensity [19] and demonstrated that achieving eradication is a choice (i.e. the actions that countries and the GPEI take matter with respect to outcomes, and neither failure nor success could be taken as a given). KRI also demonstrated the economic inefficiency of a wavering global commitment to eradication [19]. The economic analysis of post-WPV eradication immunization policies showed that either stopping OPV altogether or switching to IPV dominated the continued OPV use (i.e. control) after successful eradication of WPVs [18]. However, using IPV after WPV eradication represented the option with the highest expected costs and the lowest expected cases, while stopping poliovirus immunization represented an option with lower expected costs and some additional expected cases, which led KRI to recommend research and investment into strategies to reduce IPV costs [18]. KRI performed extensive uncertainty and sensitivity analyses [20]. Recognizing the importance of OPV cessation as an option, KRI demonstrated the need for globally coordinated coordination of OPV cessation due to game-theoretic considerations associated with cVDPV risks that could occur with uncoordinated OPV cessation [21]. This analysis also highlighted the importance of creating a stockpile for post-WPV eradication outbreak response [21]. Due to the complexity and scale of the GPEI, KRI recognized the importance of managing the GPEI as a major project and ensuring sufficient resources for polio eradication to succeed [22]. KRI discussions about this work with GPEI partners highlighted the importance of the GPEI taking the long view and asking for the funds that it needed to succeed with a long-term budget and plan, instead of what it thought it could raise in annual budgeting cycles. Although not specific to polio, by extending a simple integrated theoretical model [192], KRI discussed uncertainty and sensitivity analyses for integrated models [193] and explored the dynamics of priority shifting for eradicable diseases [194], the latter of which also built on prior KRI analysis of a wavering commitment to eradication [19]. Recognizing the importance of a stockpile of OPV for post-WPV eradication outbreak response [21], KRI developed a framework for optimal stockpile design [23]. Although KRI primarily used DEB models, KRI developed an IB polio dynamic disease transmission model that showed the significance of different assumptions about mixing networks, which remain highly uncertain and difficult to model at the global level [24].
In 2010, KRI performed an economic analysis that estimated 40-50 billion US$2013 in net benefits for the GPEI for 1988-2035. The range of estimates depended on whether successfully coordinated OPV cessation following WPV eradication included global use of IPV or not (with the lower end of the range of net benefits (i.e. less desirable) reflecting the use of IPV) [25]. That analysis assumed successful WPV eradication in 2012 and considered the impacts of a delay out to 2015 [25]. KRI contributed to discussions about the role of economic analyses in the evaluation of global disease management efforts [195] and the development of eradication investment cases [196], in book chapters not captured by the systematic review. In 2012, KRI explored trends in the risks of poliovirus transmission in the US and recognized that imported live polioviruses could potentially circulate in a population with high IPV coverage, although the risks in the US appeared low [26]. KRI also explored the probability of undetected wild poliovirus circulation after apparent global interruption of transmission [27] (by extending a simple SC model [197] developed and applied in the mid-1990s to support certification of elimination of polioviruses in the Americas [197–199]).
Still focused on post-WPV eradication and the polio endgame, as the GPEI immunization policies evolved, KRI appreciated the need to expand and update its integrated model. Specifically, as the GPEI began using mOPVs, first mOPV1 and then mOPV3, and later using bOPV (which contains both serotypes 1 and 3) for some SIAs, KRI needed to model the transmission of each serotype. KRI identified the need to model population immunity to transmission [1], and widely discussed its key role in prevention [200]. As part of its model update, KRI characterized the global immunization policy options as of 2012 and identified prerequisites for OPV cessation [28]. KRI developed a series of papers published in a 2013 special issue of Risk Analysis that described the components of its expanded and updated poliovirus transmission and OPV evolution model and discussed the role of modeling as part of the polio legacy [2]. KRI performed a comprehensive expert review of the literature on poliovirus immunity and transmission [29] and synthesized the information from the experts to (i) numerically characterize an expanded set of immunity states for its transmission model and (ii) identify significant uncertainties despite the large literature [30]. KRI reviewed the 2012 national polio immunization strategies to characterize updated prospective polio immunization policies and reviewed the seroconversion literature to characterize variability in vaccine take rates for different vaccines and numbers of doses in different settings [31]. KRI also updated its prior review of risks [13] and reviewed the literature related to understanding and modeling OPV evolution [32]. Based on this analysis [32], KRI concluded that its prior statistical model for cVDPV risks based on the historical global use of tOPV [13] offered poor predictive value of risks after the GPEI introduced mOPVs and bOPV. Specifically, the poor performance of the statistical model based on historical data [13] when compared with evidence at the time motivated KRI to include OPV evolution and the development of cVDPVs endogenously in its expanded poliovirus transmission and OPV evolution model (i.e. to use a dynamic and serotype-specific approach) [33]. KRI focused on the need to manage population immunity to transmission considering all individuals in the population, including individuals immune to disease but able to contribute asymptomatically to transmission, most notably those with only IPV-induced immunity [34]. The expanded model of poliovirus transmission and OPV evolution offered insights from modeling a diverse set of actual experiences with wild and vaccine-related polioviruses [33]. Overall, the expanded poliovirus transmission and OPV evolution model (i) uses eight recent immunity states to reflect immunity derived from maternal antibodies in infants, only IPV vaccination, only LPV infection, or both IPV vaccination and LPV infection (to more realistically capture the differences in immunity derived from IPV and LPV), (ii) includes multi-stage waning and infection processes (for more realistic characterization of these processes), (iii) characterizes OPV evolution as a 20-stage process from Sabin OPV (as administered) to fully reverted polioviruses with assumed identical properties to typical homotypic WPVs (to allow cVDPV emergence to occur within the model), (iv) characterizes each serotype separately (to analyze serotype-specific poliovirus properties, vaccination policies and risks), (v) considers explicitly both fecal-oral and oropharyngeal transmission (to account for the differential impact of IPV on fecal and oropharyngeal excretion), (vi) accounts for heterogeneous preferential mixing between mixing age groups and subpopulations, and (vii) accounts for differences between various IPV and OPV routine immunization schedules and the reality of repeatedly missed children during successive SIAs [33, 35, 36]. KRI also updated its estimates of IPV costs in the context of exploring national choices related to IPV use with various delivery options [37] and noted continued high expected costs of IPV.
KRI used the updated and expanded integrated global model to identify optimal strategies from a modeling perspective (i.e. with respect to expected health and economic outcomes) to support the GPEI partners as they worked to implement the GPEI 2013–2018 Strategic Plan [201]. In 2014, KRI modeled the dynamics of coordinated cessation of serotype 2 OPV (OPV2) without [38] and with [39] IPV, which demonstrated the importance of using sufficient amounts of tOPV in the run up to OPV2 cessation to increase population immunity to transmission prior to OPV2 cessation [38]. Despite the GPEI emphasis on IPV introduction, these analyses also demonstrated the relatively small expected role of IPV in stopping or preventing transmission in areas with conditions conducive to poliovirus transmission (i.e. relatively high R0, high contribution of fecal-oral transmission, like the countries of interest to the GPEI) [39].
Given delays in achieving eradication and requests from the GPEI partners, starting in 2013 KRI began modeling pre-eradication activities and to explore options to help accelerate eradication. KRI applied its transmission model [33] to characterize the potential impact of expanding target age groups for polio SIAs [35] and to stop and prevent poliovirus transmission in two high-risk areas in northern India [36] and in the high-risk area of northwest Nigeria [40]. Considering potential US risks, KRI developed and applied an IB model to characterize the potential for transmission of polioviruses following an introduction of a LPV into the Amish communities in North America [41]. Consistent with prior recognition of the potential for circulation of imported LPVs in areas with high IPV-only coverage based on its US modeling [26], KRI modeled population immunity to transmission and management strategies for Israel following the observation of WPV serotype 1 transmission in Israel despite its high coverage with IPV only [43]. In contrast to some other areas in the US, KRI reported relatively little heterogeneity in six counties in Central Florida at high risk of importations due to international family entertainment attractions [44]. KRI discussed some lessons from the GPEI relevant to measles and rubella eradication [45]. Insights from KRI modeling showed the importance of focusing on immunization program performance (i.e. achieving high coverage with OPV) to maintain population immunity to transmission as the key to success in the polio endgame [42]. Many KRI modeling studies emphasized the failure to vaccinate with OPV as the primary cause of delay in achieving and maintaining WPV eradication, and the importance of heterogeneity in populations that leads to pockets of preferentially-mixing under-immunized individuals that can sustain transmission [35, 36, 40, 41, 43]. KRI provided a high-level review of the policy impacts of its modeling [3].
In 2015, KRI explored the information from different types of poliovirus surveillance activities and modeled the potential for undetected live poliovirus circulation after apparent interruption of transmission [46] based on earlier exploration [27]. KRI characterized global importations and cVDPVs since 2000 and showed that over 50 countries failed to maintain sufficient population immunity to transmission to prevent paralytic cases from cVDPVs and/or imported WPVs [47]. KRI also modeled three countries that use IPV-only for routine immunization (the US, the Netherlands, and Israel) and demonstrated the decline in population immunity in transmission that occurs when countries switch from using OPV to using IPV only. At the time of global introduction of IPV beginning in OPV-using countries, KRI discussed the safety of IPV and emphasized the potential benefits of using IPV as a first dose to reduce VAPP using data from the US experience [48]. Looking closely at northwest Nigeria, KRI explored the trade-offs associated with different strategies to manage population immunity to transmission that demonstrated the high importance of using more tOPV in SIAs in the run-up to OPV2 cessation and the minimal impact of IPV [49].
KRI published a series of articles in a special issue of BMC Infectious Diseases in 2015 using its updated integrated model that aimed to help national, regional, and global health leaders navigate the polio endgame from 2013 to 2052. Modeling the long-term risks requires characterization of the potential for reintroductions of iVDPVs from a small number of individuals with B-cell-related primary immunodeficiencies [50], for which KRI reviewed the evidence collected since its 2006 statistical analysis [13]. KRI recognized that static modeling of historical data offered low predictive power for future iVDPV risks. As a result, KRI developed a DES model to support the stochastic generation of iVDPV excreters for prospective risk analyses and the exploration of the potential benefits of polio antiviral drugs (PAVDs) [50]. KRI used its iVDPV model and other stochastic risks related to containment in its integrated global model to characterize the risks, costs, and benefits of different future poliovirus risk management options for 2013–2052 compared to the 2013 baseline, which included continued widespread use of OPV for control [51]. Using both the global model [51] and a model of northern Nigeria [49], KRI showed the importance of vaccine choice and preferential use of tOPV in the run-up to globally coordinated cessation of serotype 2 OPV (i.e. OPV2 cessation), which was then-planned and since implemented in late April 2016 [52]. Recognizing the importance of significant tOPV use and sensitive to the time delays and costs of vaccine production, KRI estimated potential tOPV and bOPV needs through 2020 [53]. As global health policymakers approached the final decision point for establishing the timing of OPV2 cessation, KRI explored alternative OPV cessation and IPV introduction timing options [54] that showed substantial financial benefits associated with delayed IPV introduction. KRI demonstrated the importance of using aggressive and high-quality (i.e. rapid, high coverage, sufficiently large scope) outbreak response SIAs after OPV cessation and during the polio endgame [55]. In anticipation of coordinated OPV2 cessation, KRI explored the risks of potential non-synchronous OPV2 cessation [56] and of inadvertent tOPV use after OPV2 cessation [57]. Later work showed the potential risks of non-synchronous bOPV cessation and inadvertent use of serotype 1 or 3 OPV use after bivalent OPV cessation [58].
Using the updated integrated model [51], KRI performed an uncertainty and sensitivity analysis of cost assumptions [59] that continued to demonstrate the relatively high cost of IPV. Recognizing the importance of maintaining high population immunity for serotypes 1 and 3 prior for future coordinated bOPV cessation, KRI demonstrated the benefits of high levels of continued bOPV use and sustaining OPV production through bOPV cessation [60]. Building on prior characterization of iVDPV risks [50], KRI modeled the impact of comprehensive screening to find and treat asymptomatic iVDPV excretors and explored the impact of screening on the expected benefits of PAVDs [61]. KRI explored the potential benefits of investments in a new, ideal poliovirus vaccine assuming the best attributes of OPV and IPV [62]. Emphasizing the importance of actions taken by countries and the GPEI, KRI highlighted the importance of maintaining preparedness throughout the polio endgame [63]. KRI also demonstrated the minor role of IPV in outbreak response when used in conjunction with OPV, and showed that IPV in addition to OPV for outbreak response (in the outbreak area) does not represent a cost-effective option compared to using OPV alone [64]. KRI demonstrated the need to maintain sufficient poliovirus vaccine supplies and stockpiles for outbreak response in the polio endgame [65] and assessed the economic benefits of temporary recommendations for international travel immunization requirements for countries with transmission of WPV1 [66].
Recognizing the increasing role of environmental surveillance for polioviruses, KRI systematically reviewed published poliovirus environmental surveillance studies and reported information related to the design, cost, and effectiveness of these systems [67]. KRI also explored the dynamics of die-out of serotype 2 polioviruses after homotypic OPV cessation and lessons learned from its cessation relevant to the cessation of OPV serotypes 1 and 3 [68]. Reviewing insights from prior modeling [35, 36, 40, 41, 43], KRI demonstrated how under-vaccinated subpopulations can sustain poliovirus transmission despite high coverage in the surrounding population, depending on the degree of mixing and the size of the under-vaccinated subpopulation [69]. Building on these lessons, KRI explored the potential for silent circulation of live polioviruses in small populations [70], and the role of hard-to-reach subpopulations in characterizing the confidence about the absence of transmission for purposes of certifying the eradication of WPV1 [71]. KRI revisited its earlier characterizations of containment risks [13, 51] and explored current containment risks and their management [72]. KRI also discussed the role of system dynamics in integrated polio risk management modeling [4].
With continued failure to stop transmission in Pakistan and Afghanistan as of 2016, KRI developed a model of both countries as one epidemiologically connected area [73]. Modeling poliovirus transmission in Pakistan and Afghanistan suggested that subpopulations of under-vaccinated individuals that preferentially mix with each other probably sustain transmission and that interrupting transmission requires a significant improvement in OPV SIA coverage in these under-vaccinated subpopulations [73]. Further modeling of poliovirus transmission in Pakistan and Afghanistan suggested the need for proactive strategies (as opposed to reactive ones) to stop poliovirus transmission [74], and KRI cautioned against getting distracted by the introduction of IPV from achieving high coverage with OPV SIAs. Exploration of the potential for silent poliovirus transmission in Pakistan and Afghanistan [75] showed the role of surveillance in providing confidence about the absence of transmission. Tradeoffs in key characteristics of the poliovirus surveillance system in Pakistan and Afghanistan [76] suggest some role of environmental surveillance in assuring confidence about the absence of transmission, although KRI identified the need for further characterization of the quality of the information from polio surveillance in Pakistan and Afghanistan to fully explore the benefits of investments in environmental surveillance.
Looking prospectively at the polio endgame given failure to succeed in the GPEI objectives by 2018, KRI discussed the role of different poliovirus risks and risk management opportunities [72], and the potential risks of needing to restart OPV [77]. KRI also reflected on the role of integrated modeling to support the global eradication of vaccine-preventable diseases [4].
In 2019, KRI updated its cost estimates of the GPLN including both acute flaccid paralysis (AFP) and environmental surveillance [78]. KRI characterized the impact of hard-to-reach subpopulations on confidence about no undetected circulation in the context of supporting global certification of wild polioviruses [71]. Building on prior recognition of the potential role of a new vaccine [62], KRI commented on an article that reported the results of a new OPV2 vaccine strain (nOPV2) [79] and explored the logistical challenges of modeling and implementing a restart of OPV after its cessation [80].
Although outside of the time window for this review, in early 2020, KRI published an updated version of its integrated model to account for the programmatic experience, vaccination achieved, and epidemiology through 2019 [202]. This process included updating the inputs for its iVDPV risk model [81], and focused on actual and expected performance throughout the polio endgame instead of assuming optimistic and ideal risk management from 2015 on [203] as KRI assumed earlier [51].

4.2.  IC
Starting in 2006, IC began reporting on its application of advanced epidemiological methods to support the GPEI as part of its collaboration with the World Health Organization (WHO). IC focused on statistical analyses of existing data and data collected as part of prospective clinical trials or challenge studies and did not perform any economic analyses. With respect to transmission modeling, between 2000 and 2019, IC applied dynamic transmission models to explore several specific topics. In 2013, using a simple DEB and SC model on two hypothetical populations, IC explored IPV use after OPV cessation, which suggested that IPV would protect children from paralysis, and under some conditions, IPV use could potentially limit transmission [97]. The study also noted that IPV use in routine immunization could also potentially delay the detection of outbreaks and allow transmission to spread further by preventing AFP cases [97]. In 2014, IC used an SC model to explore the impact of older age groups on the transmission of polioviruses, which identified faster outbreak response as substantially more important than expanding the age range of campaigns [98]. IC applied the same SC model in 2017 to explore a statistical inference framework to epidemiological and genetic data collected during a poliovirus outbreak to estimate transmission parameters [99]. Using an SC model for Nigeria, in 2016 IC characterized the role of tOPV SIAs before OPV2 cessation and suggested that in closed populations with no routine immunization coverage, conducting tOPV SIAs with some characteristics (e.g. one SIA with low coverage) could increase cVDPV2 risks after OPV2 cessation [100]. The inclusion of low routine immunization coverage in the model suggested the need for a sufficient number of focused tOPV SIAs before OPV2 cessation in areas at risk of VDPV2 emergence to raise population immunity above the transmission threshold [100].
IC also used statistical models to characterize transmission dynamics. Using data from Nigerian nonpolio AFP cases, IC applied a Poisson mixed effects model to characterize the connections between local government areas (LGAs) and suggested that a radiation model of human mobility provided the best fit [101]. IC applied a similar model to data from Pakistan and found that movement dynamics did not provide strong predictors for future cases and highlighted the necessity of improved SIA quality [102].
IC performed multiple case–control studies that estimated the efficacy of poliovirus vaccines using nonpolio AFP surveillance data collected by the GPLN, many of which supported GPEI decisions to introduce additional poliovirus vaccine formulations (e.g. mOPV1, bOPV, IPV) as new tools that would accelerate eradication. The first case–control study published by IC estimated the efficacy of tOPV vaccine in India, with a focus on areas with high population density and poor sanitation (i.e. Uttar Pradesh and Bihar) in which poliovirus transmission remained endemic [82]. This analysis showed poor tOPV efficacy per dose in these areas and suggested that using some mOPV1 SIAs in these areas could help to stop WPV1 transmission without significantly increasing WPV3 risks [82]. Subsequent case–control studies estimated vaccine efficacy of mOPV1 on the order of three times higher for serotype 1 poliomyelitis disease than for tOPV for Uttar Pradesh and Bihar [83] and for polio-endemic areas in northwest Nigeria [84]. Building on this work, IC led a challenge study in northern India to assess mucosal immunity induced by OPV, which demonstrated significant differences by location, serotype, vaccine formulation, and the number of doses [85]. IC assessed rates of excretion of live polioviruses (wild and OPV-related) in asymptomatic children in contact with suspected cases as a function of age, OPV doses received, and characteristics of the suspected case, which confirmed some asymptomatic participation in WPV transmission by OPV-vaccinated children [86]. Following the introduction of mOPV1 and mOPV3 in SIAs in Nigeria, IC compared the clinical characteristics of reported polio cases, estimated vaccine efficacy for different OPV vaccine formulations, and highlighted the improvements in vaccine-induced immunity against serotypes 1 and 3 and the decline in immunity to serotype 2 in children 0–2 years of age, which resulted in increased observations of cases caused by cVDPV2s [87]. IC explored the duration of mucosal immunity induced by OPV in India and suggested that it wanes significantly within 1 year [88].
Following the introduction of bOPV, in 2012, IC performed a case–control study using data from young children in Pakistan and Afghanistan that reported comparable effectiveness of bOPV to mOPV1 for serotype 1 and commented on the poor and declining immunization coverage in these countries [89]. In 2014, IC reported on the results of trials in India that demonstrated that the delivery of a supplemental IPV dose to previously-OPV-vaccinated children <5 years old boosted their intestinal immunity [90], and does so more effectively than a supplemental OPV dose [91]. Following this study cohort, in 2017 IC reported that the duration of boosting by IPV of intestinal immunity in OPV-vaccinated children remained elevated for 6 and 11 months, but showed evidence of waning [103]. Using data from Nigeria, in 2014 IC explored the vaccine effectiveness for the different formulations of OPVs in use (i.e. mOPVs, bOPV, tOPV) and suggested that immunity in children <3 years old to serotypes 1 and 3 had improved with the use of mOPVs and bOPV [92]. In 2016, using data from Indian infants 5–11 months old, IC reported that the number of tOPV doses received represented the main determinant of serotype 3 seropositivity [104], and reported results from a clinical trial that suggested that a 3-day course of azithromycin prior to delivery did not improve the immunogenicity of mOPV3 [105]. In 2018–19, using this same population, IC reported findings that showed a correlation between the quantity of virus shed and the magnitude of the serum neutralizing antibody response at 21 or 28 days [106], showed a greater impact on OPV response by enteric viruses than bacterial microbiota [107], and that did not show an association between seroconversion from one dose of mOPV3 and FUT2 genotype (i.e. single-nucleotide polymorphisms G428A, C302 T, and A385 T) [108].
In addition to analyzing results from clinical trials and challenge studies, IC also developed statistical models to characterize risks and effectiveness of some interventions by analyzing available data. In 2011, to explore the widespread transmission of WPVs in Africa, IC applied a statistical model that identified the proximity to the continued transmission in Nigeria and poor performance of national immunization programs in some neighboring countries as risk factors for transmission of reintroduced WPVs in Africa [93]. In 2017, IC revisited this topic for both Africa and Asia, concluded that low population immunity represented a key risk factor for WPV or cVDPV transmission, and recommended maintenance or improvement of vaccination in the high-risk areas it identified [109]. In 2015, IC applied a statistical model to estimate the effectiveness of SIAs using nonpolio AFP cases reported for children <2 years old in Pakistan, which showed temporal changes in coverage and identified some under-vaccinated populations [110]. Building on this work, in 2016 IC characterized spatial and temporal trends in vaccine-induced population immunity for serotype 2 for Nigeria and Pakistan prior to OPV2 cessation to explore the need for additional serotype 2-containing vaccines [111]. In 2016, using retrospective surveillance data, IC suggested that developing a real-time database of notified AFP cases and applying a Poisson space-time scan statistic at weekly intervals could potentially lead to earlier outbreak response [112]. In 2017, a year after OPV2 cessation IC analyzed the surveillance data and concluded that high population immunity prior to OPV2 cessation facilitated the die out of serotype 2 OPV-related viruses in most areas, but that cVDPV2 circulation continued in areas at high risk for transmission [113]. IC also performed a statistical analysis that explored the impacts of using IPV in addition to OPV for outbreak response in Pakistan and Nigeria and suggested some benefit of using IPV although the results were not statistically significant [114] and an updated analysis for Pakistan in 2018 [115]. In 2018, IC analyzed different sources of routine immunization data in Pakistan that showed both variable data quality and heterogeneous coverage [116] and assessed the sensitivity of poliovirus surveillance (both AFP and ES) for serotype 1 [117].
Between 2000 and 2019, IC also contributed a number of reviews to the literature. Recognizing the wealth of studies published over decades, IC systematically reviewed the OPV challenge studies that evaluated the induction of immunity from OPV and/or IPV against shedding, which concluded that immunization with IPV would likely show limited impact on poliovirus transmission in countries characterized by fecal-oral poliovirus transmission [94]. IC discussed some of the challenges for the polio endgame with a focus on issues related to OPV vaccine failure [95], results of clinical trials performed by others that added IPV to routine immunization schedules in OPV-only using countries [118, 119] including potential impacts of IPV on mucosal immunity [120], and showing no benefits of adding IPV in mOPV2 outbreak response SIAs [121]. IC also commented on biological challenges that limit the effectiveness of vaccines in the developing world, including OPV [122], and the need for innovation in poliovirus surveillance, vaccines, and vaccination strategies [123]. IC also systematically reviewed IPV vaccine effectiveness studies [96] and the impact of IPV on mucosal immunity [124], and suggested that IPV use could play a key role in halting poliovirus transmission and hasten polio eradication due to boosting of immunity of individuals previously given OPV [124]. IC also systematically reviewed the characteristics of known iVDPVs [125], interventions to improve oral vaccine performance [126], and the effect of different vaccine schedules on humoral and intestinal immunity against poliovirus [127].

4.3.  IDM
IDM, an institute within the Global Good Fund, is a collaboration between Intellectual Ventures and Bill and Melinda Gates. IDM established a GPEI-partner collaboration with the Bill & Melinda Gates Foundation in 2011. IDM published its first polio model-related work in 2014 in a review of poliovirus infection and immunity, which it discussed in the context of developing inputs for use in an individual-based model [128]. Using an IB mathematical model, IDM explored the use of expanded age groups in SIAs and concluded that these would not significantly improve the prospects of achieving polio eradication [129]. In 2016, IDM used an IB model of children <5 years old in Kano, Nigeria, which suggested a high probability of elimination of transmission of WPV1 from Kano as of October 2015 [132]. In 2017, IDM applied an IB model of a hypothetical cVDPV2 outbreak response in northwest Nigeria, which suggested that the use of mOPV2 for outbreak response could seed new cVDPV2 lineages as early as 18 months after OPV2 cessation [133]. This analysis discussed the importance of rapid and aggressive outbreak response and the potential role of IPV, including the possibility of its use delaying detection of an outbreak [133]. In 2018, IDM described another IB model in detail and demonstrated the ability of the model to reproduce historical outbreaks in different transmission settings based on historical data [134]. IDM used this extensive and well-documented IB model to explore the stability of polio eradication after the withdrawal of OPV [134]. This analysis highlighted the fragility of eradication and the importance of strategies to stop any post-cessation outbreaks and the potential need for new vaccine tools, while suggesting a limited role for IPV in high transmission settings [134]. Building on this work, IDM used the results of a field trial in Bangladesh designed to collect fecal shedding data after mOPV2 challenge and this IB model to explore community transmission of OPV2-related viruses after OPV2 cessation, which suggested an increase in transmission risk over time after OPV2 cessation [135].
IDM also performed multiple statistical analyses using GPLN data. In 2014, IDM discussed the use of lot quality assurance sampling (LQAS) to evaluate the quality of SIAs [130] and used Nigerian AFP surveillance data to predict the risks of cases at the district level [131]. In 2015, IDM also developed a simple statistical model of the polio force of infection using data from Nigeria and based on anticipated die out of all wild poliovirus transmission in Nigeria in 2015 [136]. IDM provided a perspective on the application of advanced digital tools (e.g. GIS tracking) to fight polio and other communicable diseases [137]. In 2015, IDM also applied a heuristic algorithm to spatially reconstruct partially observed transmission networks using phylogenetic data for northern Nigeria and found substantial limitations of the method due to under-sampling [138]. Building on this work, in 2016 IDM characterized OPV revision using whole-genome sequencing data from Nigeria, which showed some evidence of transient and local transmission of OPV-related serotype 1 and 3 viruses during periods of low wild polio incidence that appeared consistent with national OPV use [139]. IDM performed a statistical analysis of immunization data to characterize OPV-induced population immunity and assess campaign effectiveness in high-risk countries to support GPEI SIA planning activities [140]. Using data from Nigeria, IDM constructed a hierarchical model to estimate SIA effectiveness to characterize OPV-induced immunity and compared these estimates to data from LQAS and incidence data [141]. Using these methods, in 2017, IDM reported spatial risk model predictions and recommended subnational prioritization to accelerate poliovirus elimination in Pakistan [142]. Following OPV2 cessation, IDM compared pre- and post-cessation detection rates of cVDPV2s and showed the die out of OPV2-related viruses in most countries [143].
In 2018, IDM reviewed its applications of IB modeling for multiple pathogens, including polio [144]. IDM also used data from Pakistan and Afghanistan to assess the sensitivity of poliovirus environmental surveillance [145]. In 2019, IDM reported the results of a cost study that compared polio eradication to indefinite control with 2 doses of IPV and multiple doses of OPV in currently OPV-using countries [146].

4.4.  Poliovirus transmission modeling studies published by other authors
In 2001, one study used a DEB model to characterize poliovirus transmission as part of an analysis that explored the probability of detecting poliovirus in sewage water as a function of different transmission conditions (e.g. equilibrium and non-equilibrium) [147]. Building on DEB modeling performed and applied prior to 2000 [204, 205], one 2001 study reported the application of a simple DEB model to characterize the expected infections and cumulative infections as a function of time since poliovirus introduction into a naïve population as a function of different net reproduction numbers ([148] see Annex). Although not captured in the review, additional perspectives by the same author published since 2000 addressed challenges for the polio endgame [206, 207], risk factors for the severity of outbreaks after eradication [208], and characterization of the extent of VDPV infections [209].
A 2005 study used a DEB model to characterize WPV in the absence of vaccines, which characterized polio as a disease of development (i.e. a disease that becomes worse as hygienic conditions improve such that individuals become infected at relatively older ages when the symptoms present as more severe) [149]. In 2008, following widespread recognition of cVDPVs, one study applied a DEB model to explore three alternative eradication strategies using pulsed OPV or continuous or pulsed IPV immunization and different levels of coverage [150]. However, this theoretical analysis ignored the benefits of secondary transmission of OPV and the complexity of reinfection and included simple modeling of the reversion of OPV given to vaccine recipients, which the authors refer to as cVDPVs but which behave more like VAPP [150]. A 2010 study by the same authors applied a DEB model that included secondary OPV transmission, which explored continuous and pulsed OPV immunization strategies [151]. A 2011 simple theoretical DEB model assumed that IPV can precipitate paralysis in a patient already incubating a poliovirus infection, and suggested sick and unimmunized children should not receive IPV during polio epidemics [152].
In 2012, a comprehensive theoretical DEB model that included OPV secondary infections, OPV evolution, and IPV use explored the dynamics of OPV cessation and the probability of eradication [153]. A 2013 study applied a DEB model that considered waning immunity and showed how countries with high transmission conditions remain at risk for epidemics from the reintroduction of WPV, which offered some explanation for challenges that prevented successful poliovirus elimination in some countries [154].
In 2015, two independent theoretical studies used DEB models to characterize the dynamics of OPV and cVDPV transmission in populations as a function of coverage and the competition for infectible individuals [155, 156]. One of these studies included an IB version of the model to simulate die out and discussion of the dynamics of small population sizes [155]. Another study in 2015 applied a simple DEB model to highlight the increasing role of reintroduction of polioviruses by travelers [157]. Another study applied an SC model to fit an SIR model to pre-vaccine US incidence data to infer WPV infection dynamics and variable time and space R0 estimates [158], which concluded that contrary to a prior study [149], polio does not appear to be a disease of development. Assuming the existence of an environmental reservoir for live polioviruses, one study characterized the impacts of different pulse vaccination strategies in a DEB metapopulation model and highlighted the importance of synchronization [160].
In 2016, one study explored the ability to detect polio cases in populations with high IPV coverage, which highlighted that asymptomatic infections may mask live poliovirus transmission and suggested longer delays to detection as vaccine coverage and/or the proportion of the population with only IPV vaccination increases [210]. Revisiting a simple theoretical model of silent circulation developed in the mid-1990s [197] and reconsidered by KRI in 2012 [27], a 2016 analysis emphasized further limitations of the simple model with respect to consideration of the vaccination history [161]. Modeling the experience with WPV1 reintroduction into Israel, one study used a DEB model to characterize the importance of using OPV to interrupt WPV transmission in a developed country with very high IPV coverage [162]. A theoretical DEB model highlights OPV as an example of a weakly transmissible vaccine for which the transmissibility of the vaccine can help with global eradication efforts [211].
One study in 2017 applied a DEB model to explore the implications of using a deployment-risk-based immunization strategy (i.e. to polio-endemic areas) for US military personnel and nondeployed US military populations [163]. Focusing on the dynamics of a hypothetical importation of WPV1 from Syria into Lebanon in 2013 to explore the potential benefits of an OPV SIA conducted in Lebanon in November 2013, a 2017 study developed an IB model that demonstrated the importance of the preventive SIA with respect to preventing a potentially large and explosive outbreak [159].
Considering the potential impacts of importations of poliovirus into IPV-using countries by large groups of immigrants, a 2017 analysis used a DEB model to explore the vaccination required in both groups to stop transmission [164].
Koopman and colleagues published multiple modeling papers between 2017 and 2019. The first study built on earlier work [154] although the 2017 analysis used a relatively simpler DEB model with much more extensive analysis of waning immunity and suggested potential challenges associated with OPV cessation due to potential silent poliovirus transmission in some areas and the potential role of environmental surveillance [165]. A separate study applied a DEB model to the importation of WPV1 in Israel and emphasized the importance of environmental surveillance [166]. A series of three papers used SC models to explore the potential for undetected transmission in theoretical small and isolated populations [167], the impact of using unrealistically high values for the basic reproduction number that limited generalization of the prior results [168], and an extension of an independent reanalysis [70] of the first paper [167] to include different assumptions about waning [169].
Recently, a 2018 study applied an IB model calibrated to stool shedding data from communities in Mexico to explore the impacts of using OPV for outbreak response 5 years after OPV cessation [170]. In 2019, one theoretical DEB modeling exercise explored the potential role of human exposure to polioviruses from the environment [171].
Although not captured by the systematic search or included in the review, readers may also find other polio models published prior to 2000 of interest. These include a DEB model of an outbreak in Taiwan [212], DEB models to support eradication planning published in 1994 [213] and 1996 [198], and three papers published in 1995–6 related to undetected circulation at the time of certification [197, 199, 214].

4.5.  Economic analyses published by other authors
The systematic search identified some additional economic analyses, and we include mention of others known to the authors. For example, the search did not find a 2003 study that estimated the costs and benefits of polio eradication by WHO region [215] or a 2004 cost analysis of potential post-eradication polio immunization policies [216], and by design, we missed economic analyses of polio eradication published prior to 2000 [217, 218]. The search included one 2000 analysis that explored pricing for combination vaccines that included IPV in the US [172]. One 2001 study reported that introducing IPV in Australia did not appear cost-effective [173], which reached conclusions similar to 1988 [219, 220] and 1996 [221] studies for the US. The search did not capture other studies that reached similar conclusions for IPV introduction in 2006 for South Africa [222] or in 2008 for OPV-using countries generally [223]. The search also did not find a 2005 study for Mexico [224] or a 2017 study for India [225] that suggested that stopping OPV SIAs and eliminating their costs could potentially off-set the costs of IPV introduction. The search captured two economic analyses published in 2006 that reported decision analysis results comparing vaccine options for responding to a poliovirus outbreak in the US from a vaccine stockpile [174] and comparing pre-vaccination serological testing vs. presumptively vaccinating internationally adopted and immigrant infants in the US [175]. The search also identified an economic analysis that explored the incentives of individual countries to participate in global polio eradication with consideration of post-eradication risks [176], which built on prior related studies by the same author not captured in the search [226, 227]. The search did not include a subsequent 2013 discussion of the multiple economic games occurring in the final stages of polio eradication [228]. The search included a 2014 study that found that switching from 10-dose to 5-dose vials of IPV reduced wastage but did not appear cost-saving for the studied vaccination facilities in Bangladesh, India (Uttar Pradesh), Mozambique, and Uganda [177]. A 2015 review of economic analyses related to disease elimination and eradication initiatives included a number of studies included in the search, but did not appear in the search results [229]. The search identified a 2016 study that estimated the health and economic benefits of three decades of polio elimination investments in India [178]. Finally, the search captured a 2017 study that reported on the GPEI costs associated with supporting tOPV-using countries as they switched to bOPV [179]. The search did not capture a 2019 study that reported the cost per child vaccinated with full versus fractional-dose IPV [230].