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].