6.  Different types of studies and their limitations
This review highlights the different types of polio transmission models developed and applied. One independent study included extensive discussion about some of the differences and limitations of models published by the three modeling groups, in particular noting the complexity of the KRI model [165]. All models depend on the scope (i.e. boundaries of the system), assumptions about structure of the system and the causal relationships that determine the equations used and the selection of model inputs, and are limited by their assumptions [203]. This section highlights some of the key differences in and limitations of the different modeling approaches.

6.1.  Dynamic, prospective, and integrated (with economics) models vs. statistical models on retrospective data or from controlled studies
KRI represents the only group that published integrated dynamic disease transmission and economic models that prospectively explore(d) the risks, costs, and benefits of strategies and policies to support the GPEI. By design, prospective models represent inherently uncertain projections into the future, and the results and insights from these models are only as good as the assumptions and the underlying available evidence. The KRI dynamic poliovirus transmission models [10, 33, 202] rely on using the available evidence and subject matter expert opinion to characterize the dynamics of poliovirus transmission as a function of differential equations, with consideration of some of the variability that exists among countries based on stratification by WBILs and relevant inputs related to transmission, seasonality, and actual vaccine use. KRI uses a model with high complexity and checks its models retrospectively to ensure that they provide estimates consistent with historical data of cases caused by WPVs and VDPVs, die out, and children with non-polio acute flaccid paralysis (NP-AFP) with a history of zero doses of vaccine, and then applies them prospectively to address policy and strategy questions [10, 33, 202]. The KRI poliovirus transmission and OPV evolution model include assumptions about a multi-stage infection process with infection stages of variable infectiousness that impacts the kinetics of infections and die-out and depends on choices about the number of stages used to model OPV evolution. These choices influence the flows of people and timing of transitions between reversion stages, while actual OPV evolution and the emergence of cVDPVs depend on random events and micro-level population dynamics [33, 202]
IDM developed and applied multiple IB models that also include considerable complexity. The first published IDM IB dynamic transmission model captures within-host susceptibility by exposure to and dose history for LPVs and/or IPV, models shedding durations and concentrations based on the host immunity histories, and assumes fecal-oral transmission among people who share a household as well as through close social contacts outside the household [129, 132, 133]. IDM applied an IB model to reproduce WPV viral shedding in different settings based on historical data [134] and added secondary spread of OPV, reinfection, and waning in some of its IB models [134, 135]. IDM does not model OPV evolution (i.e. the transition from Sabin OPV to cVDPVs) endogenously in its IB modeling [134], although Table 2 notes that IDM included statistical consideration of OPV reversion to cVDPV in one study [133]. IDM recently performed a cost study [146], but has not to date published any studies that integrated dynamic poliovirus transmission modeling with economics. IDM did not report substantial or prohibitive computational expense associated with following many individuals in IB models given the populations that it modeled to date, although IDM reported using a sampling strategy or reduced scope model to avoid computational burden in some of its IB modeling papers [132, 133].
IC did not consider economics in any of its modeling. As shown in Table 1, IC developed a few SC models and applied them prospectively to address specific questions. However, most of the publications by IC present statistical analyses of existing, retrospective data with a focus on answering specific questions driven by the data. Extrapolation of the results and inferences from statistical models requires assuming that the data collected in the past provide a good representation of the future and directly relate to the question asked. With eradication efforts driving cases to zero, epidemiological models lose their ability to make inferences based on comparing observed retrospective cases for different interventions, because as the polio cases disappear the data become sparse and controlling the data for confounders and other biases becomes difficult. The case–control epidemiological methods used by IC remain highly sensitive to the selection of cases and controls, and any limitations associated with the data used to perform the analyses.
In addition, in the context of complex dynamic systems, statistical models can provide relatively poor insight about prospective risks. For example, in the early 2000s, when countries only used tOPV (i.e. no mOPV or bOPV), KRI characterized the risks of cVDPVs using a statistical model [13]. However, a subsequent review of available data demonstrated the inadequacy of this approach following the introduction of mOPV and bOPV, which created substantial immunity gaps for serotype 2, and increased the risks of cVDPV2s [32], which led KRI to add OPV evolution endogenously into its dynamic transmission model [33, 202].

6.2.  Different assumptions for modeling populations and mixing
As shown in Tables 2 and 3, the models reviewed differed with respect to the populations modeled and the mixing assumptions used. DEB and SC models typically assume homogeneous mixing of individuals in a population, although they may account for preferential mixing by age, subpopulation, or other factors, and include births, deaths, aging, and immigration. Part of the complexity of KRI transmission models comes from the use of population-specific demographic and immunization history data for inputs and the inclusion of preferential mixing by age and/or subpopulation. The inclusion of undervaccinated subpopulations in DEB models probably only partially captures some of the population heterogeneity in under-vaccinated communities, but does so better than ignoring this heterogeneity for some analytical questions.
IB models seek to capture the full richness of the complexity of transmission, but they do so with considerable computational costs. IB models track each individual in a population, which can offer advantages that include simulating die-out directly, but require many assumptions about the spatial distribution and contact patterns for each individual in the model [24, 41].
One limitation of transmission models broadly arises from assumptions about mixing at the model boundaries. Most models characterize transmission within a closed population, but they can allow for importations and exportations of viruses as appropriate [33, 202].

6.3.  Different assumptions for die out
DEB models use simplified population structures and fractional rate-based processes that allow for fractional individuals, which requires the use of a transmission threshold to simulate die-out [10, 33, 202]. In real populations, the die out of transmission involves some element of chance. For analyses that focus on low levels of transmission and die out (e.g. analyses about the confidence of no undetected circulation), the modeling groups typically apply SC models to simulate the stochasticity of die out, although they have used both types of stochastic simulation approaches.