3.  Results
Following the search process shown in Figure 1, the systematic literature review and addition of other studies by the three GPEI-supported modeling groups led to the extraction of information from 176 included studies [1-4, 8-179]. As noted, during review of the full text of the studies identified by the search, we excluded papers that presented statistical analyses that did not include a mechanistic poliovirus transmission model [180–187].
Table 1 summarizes some attributes of the included studies. Not surprisingly, the number of publications by each modeling group reflects the beginning of their efforts (i.e. KRI 78 papers since 2003, IC 46 papers since 2006, and IDM 19 papers since 2014). Similarly, as the number of modeling groups increased, so did the number of publications per 5-year time period (i.e. 5 papers 2000–2004, 22 papers 2005–2009, 45 papers 2010–2014, and 103 papers from 2015 to 2019). All of the modeling groups developed and applied some dynamic transmission models, although the extent of these efforts varied considerably. For example, only KRI combined dynamic transmission and economic modeling into integrated policy models and used all of the different types of dynamic transmission modeling tools (i.e. DEB, SC, IB, and DES). In addition, the three modeling groups tend to preferentially apply different modeling tools (i.e. DEB modeling dominates for KRI, SC for IC, and IB for IDM). We did not include studies that performed statistical simulation of infections (e.g. [136]) as dynamic transmission models. As shown in Table 1, all of the modeling groups also published papers that did not include transmission modeling or economic analyses. Notably, IC invested considerable efforts in characterizing vaccine effectiveness based on clinical trial and surveillance data, and on characterizing risks using statistical epidemiology to support inferences. Table 1 shows multiple reviews performed by all of the modeling groups to develop inputs for their transmission models. Table 1 also includes the contributions to the literature from others, which largely represent single papers, but with notable exception of multiple papers by Professor James Koopman (University of Michigan).
Table 1. Characteristics of included peer-reviewed polio-related studies published in English 2000–2019.
Characteristic  
Modeling group KRI (n = 78) [1-4, 8-81]IC (n = 46) [82–127] a,bIDM (n = 19) [128–146]Poliovirus transmission modeling by others (n = 24) [147–171]Economic analyses by others (n = 9) [172–179]
Publication date 2000–2004 (n = 5) [8, 147, 148, 172, 173]2005–2009 (n = 22) [9-22, 82–86, 149, 150, 174, 175]2010–2014 (n = 45) [1, 2, 23–42, 87–98, 128–131, 151–154, 176, 177]2015–2020 (n = 103) [3, 4, 43–81, 99–146, 155–171, 178, 179]
Publication type Integrated (DEB transmission and economic combined) (n = 12) [9, 18–20, 25, 51, 54, 59, 61, 62, 64, 65]Dynamic transmission only (n = 70) c,dDEB (n = 45) [10, 14, 22, 26, 33–36, 38–40, 43, 47, 49, 52, 53, 55–58, 60, 68, 69, 73, 74, 77, 97, 147–157, 160, 162–166, 171] cSC (n = 15) [27, 46, 70, 71, 75, 76, 97–100, 147, 158, 161, 167–169]IB (n = 10) [24, 41, 129, 132–135, 155, 159, 170]dDES,DEB (n = 3) [4, 50, 81]Economic/cost analysis only (n = 15) [11, 12, 21, 23, 66, 78, 146, 172–179]Statistical analyses (by 3 GPEI-supported modeling groups only) (n = 38)Risk assessment (n = 19) [44, 93, 101, 102, 109–113, 116, 117, 130, 131, 136, 140–143, 145]Vaccine effectiveness (n = 17) [82–84, 87–92, 103–108, 114, 115]Mucosal immunity (n = 2) [85, 86]Reviews (by 3 GPEI-supported modeling groups only) (n = 14)Transmission model inputs (n = 11) [13, 29, 30, 32, 94, 96, 126–128, 138, 139]Risk model inputs (n = 3) [67, 72, 125]Discussions (by 3 GPEI-supported modeling groups only) (n = 26)Policy options (n = 5) [8, 28, 31, 37, 80]Perspectives (n = 13) [1-3, 15–17, 45, 63, 95, 122, 124, 137, 144]Commentaries (n = 8) [42, 48, 79, 118–121, 123]
Abbreviations: DEB, differential-equation-based model; DES, discrete-event simulation model; IB, individual-based model; IC, Imperial College; IDM, Institute for Disease Modeling; IPV, inactivated poliovirus vaccine; iVDPVs, immunodeficiency-associated vaccine-derived poliovirus; KRI, Kid Risk, Inc.; OPV, oral poliovirus vaccine; SC, stochastic compartmental model; SIAs, supplementary immunization activities.
Notes
aTwo papers included one middle author from IDM [100, 109].
bOne author on three papers now at the London School of Hygiene and Tropical Medicine [116, 117, 127].
cTwo papers included both DEB and SC model formulations [97, 147].
dOne paper included both DEB and IB model formulations [155].
Table 2 provides an overview of some of the attributes of the model structures and assumptions for the 83 papers that included a poliovirus transmission model [4, 9, 10, 14, 18–20, 22, 24–27, 33–36, 38–41, 43, 46, 47, 49–62, 64, 65, 68–71, 73–77, 81, 97–100, 129, 132–135, 147–171] organized by modeling group. Mathematical models for poliovirus transmission vary considerably in their complexity. The review identified papers that ranged from analytical exploration of theoretical issues using hypothetical populations for an average poliovirus to papers that simulated all of the complexity that comes with seasonal transmission of three serotypes of LPVs in populations with complicated national immunization strategies and histories. Table 2 shows the counts of and references for papers that modeled the transmission of outbreak viruses only, transmission of WPV, cVDPV, and/or OPV viruses, and those that included endogenous OPV evolution and model all LPVs. Table 2 also identifies the papers that included different attributes, including consideration of seasonality, specific-serotype transmission model inputs, OPV secondary spread, VAPP, both fecal-oral and oropharyngeal transmission routes, waning immunity, reinfection, and/or boosting OPV-induced immunity by IPV. With respect to mixing, Table 2 also captures whether each model included more than one age group and/or subpopulation and whether it included heterogeneous preferential mixing between age groups and/or subpopulations. With highly variable model structures, Table 2 identifies papers that included multiple immunity states to account for differences in immunity induced by OPV and IPV (in some cases as a function of the dose history), and immunity derived from maternal antibodies in infants. Table 2 also noted the papers with models that included one or more latent (i.e. infected but not infectious) stages and whether the models used a multi-stage infection process. DEB transmission models with a single stage for infection can lead to unrealistically short durations for many infections and long tails for others [188], which motivates the use of multi-stage infection processes in DEB models. SC models can avoid the issue of exponential departure rates from a single infection stage by using distributions instead of multiple stages (i.e. they simulate multi-stage infection processes more directly), and IB models may use time-varying functions for individual agents to model infections. DEB models can be solved analytically for some simple models or simulated numerically. SC models involve different types of stochastic simulation, which include following every single transition that occurs in the population with variable time steps [189], or using draws from an appropriate probability distribution (e.g. Poisson) to randomly determine the number of transitions that occur in the system during a fixed time step [188]. IB models simulate individual agents, and DES models track events. Remarkably, the review also identified a few theoretical papers that included an environmental reservoir, which is not consistent with the epidemiological experience with polioviruses. Finally, Table 2 also provides a high-level perspective on the types of immunization included in each paper by noting the studies that included OPV in RI, OPV in SIAs, IPV in RI, and IPV in SIAs, the studies that account for differences between various IPV and OPV RI schedules, and that account for the reality of repeatedly missing the same children during successive SIAs.
Table 2. Numbers of papers with specific characteristics of dynamic transmission models by group among 83 papers with such models.
Characteristic KRI IC IDM Other
Transmission models 49 a,b [10, 27, 70] 4 [97–100] 5 [129, 132–135] 24 [147–171]
WPV, cVDPV, and/or OPV outbreaks (only) 1 [70] 3 [97–99] 1 [132] 9 [147, 148, 152, 157–159, 167–170]
WPV, cVDPV, and/or OPV transmission 11 a [10, 27] 1 [100] 3 [129, 134, 135] 13 [149–151, 154, 156, 160–166, 171]
All LPVs transmission and OPV evolution 37 b   1 [133] 2 [153, 155]
Models that include specific complexities
Seasonality 47 a,b [10]   1 [132] 4 [158, 160, 162, 163, 166]
Specific-serotype transmission model inputs 39 b [10, 27] 3 [98–100] 5 [129, 132–135] 5 [161, 162, 165, 166, 170]
OPV secondary spread 48 a,b [10, 27] 1 [100] 4 [129, 133–135] 8 [151, 153–155, 161, 165, 166, 170]
VAPP 46 a,b     1 [150]
Fecal-oral and oropharyngeal transmission separately 37 b      
Waning 46 a,b   3 [129, 134, 135] 3 [154, 163, 165]
Reinfection 46 a,b   3 [129, 134, 135] 3 [154, 163, 165]
Boosting of immunity by IPV 46 a,b   3 [134, 135]  
Multiple age groups 45 c 1 [98] 3 [129, 132, 134] 5 [149, 154, 158, 159, 165, 170]
Subpopulations 34 d   2 [129, 132] 4 [159, 160, 163, 164]
Heterogeneous preferential mixing between age groups 45 c 1 [98] 1 [132] 1 [159]
Heterogeneous preferential mixing between subpopulations 34 d   2 [132, 133] 2 [159, 163]
Models that include specific states
Different immunity states for OPV and IPV if model includes both 48 a,b [10, 27]     3 [153, 161, 163]
Multiple immunity states for immunity induced for different OPV and/or IPV dose histories 37 b   5 [129, 132–135] 1 [162]
Maternal antibodies in infants 37 b   5 [129, 132–135] 1 [158]
1 or more latent stages (infected not infectious) 48 a,b [10, 27] 3 [97–99]   9 [151, 152, 156, 159, 161–163, 166, 170]
Multi-stage infection processes 38 b [27]   5 [129, 132–135] 2 [151, 161]
Environmental reservoir       3 [149, 160, 171]
Vaccination considered
OPV in RI 48 a,b [10, 27] 1 [100] 5 [129, 132–135] 13 [150, 151, 153–157, 159, 161, 163–165, 171]
OPV in SIAs 45 b [10, 14, 18–20, 22, 24, 25] 2 [98, 100] 5 [129, 132–135] 8 [150, 151, 155, 159, 160, 162, 166, 170]
IPV in RI 38 b [10] 1 [97] 2 [133–135] 8 [150, 152, 153, 159, 161, 163, 164, 170]
IPV in SIAs 9 [51, 55, 59, 64, 68, 73–76]   1 [133] 1 [150]
Differences in OPV and IPV RI schedules 37 b   5 [129, 132–135]  
Repeatedly missed children in successive SIAs 37 b 1 [100]    
Abbreviations: cVDPV, circulating vaccine-derived poliovirus; IC, Imperial College; IDM, Institute for Disease Modeling; IPV, inactivated poliovirus vaccine; KRI, Kid Risk, Inc.; LPV, live poliovirus; OPV, oral poliovirus vaccine; RI, routine immunization; SIAs, supplementary immunization activities; VAPP, vaccine-associated paralytic polio; WPV, wild poliovirus.
a All of the following: [9, 14, 18–20, 22, 24–26].
b All of the following: [4, 33–36, 38–41, 43, 46, 47, 49–62, 64, 65, 68, 69, 71, 73–77, 81].
c All of the following: [4, 9, 10, 14, 18–20, 22, 24, 26, 33–36, 38–41, 43, 46, 47, 49–62, 64, 65, 68, 71, 73–77, 81].
d All of the following: [4, 10, 26, 35, 36, 40, 43, 46, 47, 49–62, 64, 65, 68, 69, 71, 73–77, 81].
Table 3 summarizes the populations considered by the 83 papers that included a polio transmission model [4, 9, 10, 14, 18–20, 22, 24–27, 33–36, 38–41, 43, 46, 47, 49–62, 64, 65, 68–71, 73–77, 81, 97–100, 129, 132–135, 147–171] organized by modeling group. The search process revealed a wide range of populations explored. KRI represents the only modeling group that developed and applied a global model, which relates to its focus on global policy. As shown in Table 3, multiple groups modeled the same countries, particularly the polio-endemic countries as of 2006 (i.e. India, Nigeria, Pakistan, and Afghanistan). For each entry, Table 3 shows the population size or time series of population size modeled (N) and the R0 used when reported (i.e. entries missing this information did not report it). Values of R0 depend on the population, model structure, and poliovirus serotype, so comparisons between different modeling groups for a given population should consider the different attributes of the models identified in Table 2.
Table 3. Populations modeled in dynamic transmission models in 83 papers by group, showing population size (N, in millions (M)) (for the time or time series used) and basic reproduction number (R0), if reported.
Population KRI IC IDM Other
Global N = 6,826–8,072 M (2010–2029), R0 = 4–13 by WBIL [18, 20]N = 2,526–9,640 M (1950–2100), R0 = 4–13 by WBIL for WPV1, WPV1*0.9 for WPV2, WPV1*0.75 for WPV3 [4, 50–62, 65, 77, 81]      
Country group*        
104 GPEI countries N = 3,600 M in 1988, R0 = 7.5 (LI), 9.5 (LMI), 11.5 (UMI) [25]      
Low-income countries N = 2,933–3,992 M (2010–2029), R0 = 10 or 13 [19, 22]      
16 African countries       R0 = 1.2–3 for cVDPV2 [133]
European countries       [164]
Importation countries       N = 613 M (2013), R0 = V [157]
GPEI polio-endemic countries (as of 2006)
India (Uttar Pradesh and Bihar) N = 247 M (2006), R0 = 16 [19]N = 54–224 M (1950–2100), R0 = 13 [33]N = 55–224 M (1950–2100), R0 = 13 [35, 36, 46]   [134]  
Nigeria N = 9.7–186 M (northwest zone, 1950–2100), R0 = 8 [33]N = 9.7–234 M (northwest zone, 1950–2100), R0 = 7.5 [35, 40, 46, 49, 64] N = 0.01 M, R0 = 5 [100] [133]N = 0.3 M [129]N = 1.8 M (Kano, 2016), R0 = V [132]  
Pakistan and/or Afghanistan N = 45–422 M (1950–2100), R0 = 11 [71, 73–76]      
Other countries modeled by at least one GPEI-supported modeling group
Israel N = 1.3–15 M (1950–2100), R0 = 5–6 [43, 46, 47]     N = 0.050–0.067 M (2012–2014), R0 = 1–10 [162]N = 100%, R0 = 1.62 [166]
Tajikistan N = 1.5–11 M (1950–2100), R0 = 7–8 [33]N = 1.5–21 M (1950–2100), R0 = 8 [35, 46] N = 5.6 M, R0 = 2.16–2.46 [98]N = 5.6 M, R0 = 2.58 [99]    
United States of America N = 145–570 M (1950–2100), R0 = 6 [9]N = 318–346 M (2010–2020), R0 = 6 [26]N = 158–478 M (1950–2100), R0 = 5 [33]N = 0.276 M (2013 Amish), R0 = 5 [41]N = 158–462 M (1950–2100), R0 = 5 [47]   Houston, Louisiana [134] N = 0.05–0.09 (deployed military personnel 2015–2025), R0 = V [163]R0 = V [158]
Other countries modeled
Albania N = 3.2 M (1996), R0 = 11 [10]N = 1.2–1.8 M (1950–2100), R0 = 11 [33]      
Bangladesh (Matlab)     N = 0.13 M (2012) [135]  
Cuba N = 5.9–7.0 M (1950–2100), R0 = 8 [33]      
Dominican Republic N = 3.6 M (2000), R0 = 11 [10]      
Haiti N = 3.2–14.6 M (1950–2100), R0 = 9.5 [33]      
Indonesia (Madura Island) N = 74–254 M (1950–2100), R0 = 9 [33]      
Lebanon       N = 7 M (2015) [159]
Mexico (Campo Grande, Capoluca, Tuxpanguillo)       R0 = V [170]
The Netherlands N = 15.2 M (1996), R0 = 5 [10]N = 10–17 M (1950–2100), R0 = 4 [33]N = 10–16 M (1950–2100), R0 = 5 [47]      
Republic of the Congo   N = 2.8 M, R0 = 1.5–1.85 [98]    
Theoretical or hypothetical populations N = 100 M, R0 = 4–13 by WBIL [10]N = 10 or 100 M, R0 = 6–13 [14]N = 0.1 M, R0 = 13 [24]N = 0.1–1 M, R0 = 8–16 [27]N = 1 M, R0 = 10 [34, 69]N = 1 M, R0 = 3.6–11.7 [38, 39]N = 0.0035–0.01 M, R0 = 15,20,25 [70] N = 1 M, R0 = 3,10 [97]   R0 = V [147, 148, 151, 152, 156]N = 100%, R0 = 2.8 [149]N = 100%, R0 = 4–20 [154]N = 100%, R0 = 14 [160, 171]N = 100% (DEB), 0.001–0.1 M (IB), R0 = V [155]N = 100 M, R0 = 6 [150]N = 100 M, R0 = V [153]N = 0.2 M, R0 = 8–16 [161]N = 1 M, R0 = V [165]N = 0.0035–0.01 M, R0 = 15,20,25 [167–169]
* See source for list of included countries.
Abbreviations: cVDPV(1,2,3), circulating vaccine-derived poliovirus(serotype 1, 2, or 3); DEB, differential-equation based; IB, individual-based; GPEI, Global Polio Eradication Initiative; IC, Imperial College; IDM, Institute for Disease Modeling; IPV, inactivated poliovirus vaccine; KRI, Kid Risk, Inc.; LI, low-income countries; LMI, lower middle-income countries; M, million; N, population; R0 basic reproduction number; UMI, upper middle-income countries; V = varied (used for R0 values, see paper); WBIL, World Bank Income Level; WPV(1,2,3), wild poliovirus(serotype 1, 2, or 3).