Review of poliovirus modeling performed from 2000 to 2019 to support global polio eradication

Figures & data

Figure 1. Literature search process.

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,b IDM (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,d DEB (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] ^c SC (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]^d DES,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. 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. 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).

Table 4. Summary of themes explored by multiple modeling groups.

Theme	KRI	IC	IDM	Other
Outbreak response speed	[14, 35, 43, 55]	[98]		[162, 166]
Expanded age group SIAs	[35]	[98]	[129]
Population immunity*	[10, 16, 18, 19, 26, 33–40, 43, 46, 47, 49, 52–58, 60, 68–70, 73–77]	[83, 84, 87, 89, 92, 93, 100–102, 109, 111]	[131, 133, 140–142]	[155, 162]
OPV cessation dynamics	[26, 38, 39, 49, 68]	[100, 111, 113]	[134, 143]	[153, 165, 166]
Silent transmission on an IPV background and/or delayed detection of transmission due to IPV use	[26–28, 39, 41]	[97]	[133]	[162, 164, 166, 170]
Role of IPV after OPV cessation	[18–20, 25, 28, 33, 39, 51–60, 64, 65, 68, 69, 73–77, 80]	[90, 91, 94, 97, 103, 114, 115, 118–120, 122]	[133]	[153]
Undetected circulation	[27, 46, 70, 71, 75, 76]		[132, 136]	[161, 165, 167–169]
Role of IPV in outbreak response SIAs	[51, 55, 64, 68]		[133]	[150, 164]
Environmental surveillance	[43, 46, 55, 67, 71, 73–76, 78]	[117]	[136, 145, 147]	[162, 166]
Vaccine stockpile	[21, 23, 53, 65, 77]			[174]
iVDPVs	[4, 13, 50, 61, 81]	[125]

Abbreviations: 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; SIAs, supplementary immunization activities.

* As indicated in text, defined differently by the 3 modeling groups: KRI focuses on modeling infection and defines ‘population immunity to transmission’ based on all individuals of all ages integrated over all immunity states in a DEB model as a function of serotype, population-specific inputs, and time, which is a model-based concept that does not vary by paper (see details in [34, 202]). KRI publications earlier than 2013 discussed ‘population immunity’ as the same concept (i.e. over the entire population), but characterized it as an input for some analyses based on data (see e.g. [10]); IC focuses only paralysis (i.e. not infection) and defines ‘population immunity’ including only vaccine-induced immunity (i.e. excluding immunity from maternal antibodies and immunity induced by infection with any live poliovirus via community spread), and varies by paper depending on the data used (e.g. nonpolio AFP data for: serotype 1 only for children <5 years old [83, 84, 87], serotypes 1 and 3 for children <2 years old [89], serotypes 1, 2, and 3 for children <36 months [92], serotype 1 for children <5 years old [101], serotype 2 for children <2 years [100], serotype 2 for children <36 months [111, 113], and serotype 1 for children <36 months [102]; multiple metrics used for regression analyses [93, 109], see individual papers for specific definitions); IDM definition of ‘population immunity’ includes only vaccine-induced immunity (i.e. excluding immunity from maternal antibodies and immunity induced by infection with any live poliovirus via community spread), focuses on paralysis (i.e. not infection), and varies by paper depending on data used (e.g. OPV-induced immunity for nonpolio AFP cases in children <5 years old in a district within a 6-month period [131, 133, 141, 142], children <15 years old [140], dose estimates based on SIAs, see individual papers for specific definitions).

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