. Author manuscript; available in PMC: 2025 Jan 4.

Published in final edited form as: Risk Anal. 2013 Mar 22;33(4):703–749. doi: 10.1111/risa.12044

Table I.

Generic Model Inputs for an Expanded Poliovirus Transmission Model

Model input (symbol)	Best estimate	Source	Notes

Characterization of recent immunity states:
Relative susceptibility (σ) of recent immunity states (for PV1;PV2;PV3)		18,19	“Probability of homotypic poliovirus infection in a recent immunity state divided by the probability of homotypic poliovirus infection in fully susceptible individuals, given identical exposure,”⁽¹⁹⁾ based on means of 9 expert assessments⁽¹⁹⁾
- Maternally immune	0.78;0.79;0.77
- 1 successful IPV	0.91;0.92;0.90
- 2 successful IPV	0.80;0.80;0.79
- ≥ 3 successful IPV	0.72;0.72;0.71
- 1 LPV infection	0.42;0.43;0.41
- ≥ 2 LPV infections	0.21;0.22;0.20
- IPV and LPV	0.21;0.22;0.20
Duration of latent period ( $ξ^{f e c}$ or $ξ^{o r o}$ , in days)	∼ 3^a	18,19	Average time between LPV exposure and becoming infectious, based on means of 9 expert assessments⁽¹⁹⁾ and assumed equal for all waning stages
Duration of fecal infectiousness ( $γ^{f e c}$ , in days) of recent immunity states (for PV1;PV2;PV3)		18,19	“Average length of time of [fecal] excretion of sufficiently high concentrations of virus for infectiousness to others,”⁽¹⁹⁾ based on means of 9 expert assessments⁽¹⁹⁾
- Fully susceptible	28.0;27.8;28.3
- Maternally immune	24.6;24.6;24.6
- 1 successful IPV,	24.5;24.4;24.7
- 2 successful IPV	21.1;20.8;21.3
- ≥ 3 successful IPV	18.0;17.7;18.2
- 1 LPV infection	11.6;10.5;10.5
- ≥ 2 LPV infections	10.1;8.9;8.9
- IPV and LPV	10.1;8.9;8.9
Duration of oropharyngeal infectiousness ( $γ^{o r o}$ , in days) of recent immunity states (no serotype differences)		18,19	“Average length of time of [oropharyngeal] excretion of sufficiently high concentrations of virus for infectiousness to others,”⁽¹⁹⁾ based on means of 9 expert assessments⁽¹⁹⁾
- Fully susceptible	13.4
- Maternally immune	11.9
- 1 successful IPV	9.9
- 2 successful IPV	6.6
- ≥ 3 successful IPV	6.1
- 1 LPV infection	5.0
- ≥ 2 LPV infections	3.7
- IPV and LPV	3.7
Relative fecal infectiousness $(π^{f e c})$ of recent immunity states (for PV1;PV2;PV3)		18,19	Computed as relative contribution to fecal transmission compared to fully susceptible individuals,⁽¹⁹⁾ divided by relative duration of fecal infectiousness compared to fully susceptible individuals
- Maternally immune	0.96;0.96;0.95
- 1 successful IPV	0.92;0.92;0.91
- 2 successful IPV	0.70;0.69;0.68
- ≥ 3 successful IPV	0.61;0.59;0.59
- 1 LPV infection	0.39;0.43;0.43
- ≥ 2 LPV infections	0.20;0.23;0.23
- IPV and LPV	0.20;0.23;0.23
Relative oropharyngeal infectiousness $(π^{o r o})$ of recent immunity states (no serotype differences)		18,19	Computed as relative contribution to oropharyngeal transmission compared to fully susceptible individuals;⁽¹⁹⁾ divided by relative duration of oropharyngeal infectiousness compared to fully susceptible individuals; for the IPV-only states, we divided the expert-based estimate by 2 to obtain roughly similar oropharyngeal infectiousness as LPV states after accounting for higher relative susceptibility in the IPV-only states
- Maternally immune	0.68
- 1 successful IPV	0.30
- 2 successful IPV	0.17
- ≥ 3 successful IPV	0.12
- 1 LPV infection	0.33
- ≥ 2 LPV infections	0.21
- IPV and LPV	0.21
Number of infection stages			Fitted such that approximately 1:600 fully susceptible individuals remain fecally infectious after 90 days (see Appendix A2);⁽⁴⁵⁾ assumed equal for all immunity states and waning stages
- Latent period (r)	2
- Infectious period (s)	4
Relative weight of infection stages, compared to average weight over the infectious period $(θ_{j}, j = 0, \dots, r + s - 1)$		18,19	Values obtained by fitting to elicited relative contribution to transmission over time from experts for fecally infectious fully susceptible individuals (see text and Appendix A2)
- Infection stage 0 and 1 (latent stages)	0
- Infectious stage 2	12/17
- Infectious stage 3	40/17
- Infectious stage 4	12/17
- Infectious stage 5	4/17
IPV immunity delay ( $ϕ$ , in days)	7	13	Average time between successful IPV administration and acquisition of properties of next IPV state
Characterization of waning of immunity to poliovirus transmission:
Number of waning stages ( $n w$ )	5		Includes recent stage; model choice intended to reasonably represent continuous waning process
Shape of waning function ( $z_{w}$ )	5	18,19	Shape parameter in waning function (see methods section and Appendix A2)
Average time to reach last waning stage ( $ρ$ , in days)		18,19	Based on informed judgment and model calibration; only applies to active immunity (i.e., not to maternally immunes); fastest waning for type 3 given typically lower antibody titers over time after infection or vaccination^(46–49)
- Type 1&2	4 × 365
- Type 3	3 × 365
Average time for maternal immunes to wane to fully susceptible ( $ρ_{M I}$ , in days)	0.25 × 365	18,19	Model choice to approximate patterns elicited from 9 experts;⁽¹⁹⁾ this value corresponds to the width of the first age group
Relative susceptibility ( $σ$ ) for last waning stage (no serotype differences)		18,19	Based on informed judgment and model calibration
- 1 successful IPV	1.0
- 2 successful IPV	1.0
- ≥ 3 successful IPV	1.0
- 1 LPV infection	0.8
- ≥ 2 LPV infections	0.7
- IPV and LPV	0.7
Duration of fecal infectiousness ( $γ^{f e c}$ , in days) of last waning stage (for PV1;PV2;PV3)		18,19	Computed such that relative duration equals relative infectiousness for last waning stage compared to fully susceptible individuals; for “≥ 2 LPV infections” and “IPV and LPV”; this approach would imply shorter durations of infectiousness for the last waning stage than for the recent immunity state, and therefore we assigned duration values directly such that the product of relative infectiousness and relative duration equals 0.1225 ( = 0.35²) based on informed judgment and model calibration
- 1 successful IPV	26.6;26.4;26.9
- 2 successful IPV	25.2;25.0;25.5
- ≥ 3 successful IPV	23.8;23.6;24.1
- 1 LPV infection	14.0;13.9;14.1
- ≥ 2 LPV infections	11.4;11.4;11.6
- IPV and LPV	11.4;11.4;11.6
Duration of oropharyngeal infectiousness ( $γ^{o r o}$ , in days) of last waning stage (no serotype differences)		18,19	Computed such that relative duration equals relative infectiousness for last waning stage compared to fully susceptible individuals; for “≥ 3 successful IPV,” this approach would imply shorter durations of infectiousness for the last waning stage than for the recent immunity state, and therefore we assigned duration values directly such that the product of relative infectiousness and relative duration equals 0.1225 ( = 0.35²) based on informed judgment and model calibration
- 1 successful IPV	11.4
- 2 successful IPV	6.7
- ≥ 3 successful IPV	6.6
- 1 LPV infection	6.7
- ≥ 2 LPV infections	4.0
- IPV and LPV	4.0
Relative fecal infectiousness ( $π^{f e c}$ ) of last waning stage (no serotype differences)		18,19	Based on informed judgment and model calibration
- 1 successful IPV	0.95
- 2 successful IPV	0.9
- ≥ 3 successful IPV	0.85
- 1 LPV infection	0.5
- ≥ 2 LPV infections	0.3
- IPV and LPV	0.3
Relative oropharyngeal infectiousness ( $π^{o r o}$ ) of last waning stage (no serotype differences)		18,19	Based on informed judgment and model calibration
- 1 successful IPV	0.43
- 2 successful IPV	0.25
- ≥ 3 successful IPV	0.13
- 1 LPV infection	0.5
- ≥ 2 LPV infections	0.3
- IPV and LPV	0.3
Characterization of OPV evolution:
Number of reversion stages (h)	20		Stage 0 = OPV; stage h−1 = FRPV
Shape of reversion function with respect to:			Shape parameter in reversion function that characterizes increase in R₀ and ln(PIR) as a function of the reversion stage (see methods section and Appendix A2)
- R₀ ( $z_{r}$ )	1
- ln(PIR) ( $z_{p}$ )	2.5
Average time to reach last reversion stage ( $ε$ , in days) (for PV1;PV2;PV3)	547.5; 360; 547.5		Based on assumption that OPV-related virus attains identical properties as typical homotypic WPVs after it reaches 1.5 times the GPLN threshold^(4,17,121) of 10 (PV1&3) or 6 (PV2) nucleotide changes occurred in the VP1 region, with 10 assumed nucleotide changes per year⁽¹²²⁾
Paralysis-to-infection ratio for fully susceptible individuals infected with OPV (PIR₀) (for PV1; PV2;PV3)	0.26 × 10⁻⁶; 1.2 × 10⁻⁶ 1.8 × 10⁻⁶		Calibrated to USA VAPP data by dividing the estimated type-specific incidence of recipient VAPP 1980–1996 (CDC, unpublished data) by the total number of recipient OPV infections during the same time period
Paralysis-to-infection ratio for fully susceptible individuals infected with FRPV (PIR_h-1) (for PV1; PV2;PV3)	0.005; 0.0005; 0.001	13,25	Assumes similar PIRs for FRPVs as typical homotypic WPVs
Relative R₀ of OPV vs. FRPV ( $τ_{0}$ ) (for PV1; PV2; PV3)	0.37;0.56;0.25	18,19	Based on literature review, expert elicitation, and model calibration
Other inputs:
Effective infectious proportion below which we assume 0 force-of-infection (transmission threshold EPI*)	5/1,000,000		Based on judgment and model calibration to produce approximately correct timing of die-out in the DEB model (see text); assumed equal for all reversion stages and mixing age groups
Relative PIR for maternally immunes compared to fully susceptible individuals (RPIR_MI)	0.5		Based on calibration of the USA model to the observed median age of 3 months for recipient VAPP during 1980–1996 (CDC, unpublished data)
Ratio of R₀ by serotype in the same setting (PV1:PV2:PV3)	1:0.9:0.8		Assumption based on relatively low frequency of WPV3 importations or cVDPV3 outbreaks despite generally low observed type 3 antibody levels,^(46–49) and model calibration
Average incubation period ( $δ$ , in days)	10	13,123	Average time between entering first latent stage and onset of paralysis for paralytic poliomyelitis patients
Demographics for all situations	Time series 1950–2100	61	Death rates fitted to UN Population Division’s medium variant estimates of population by age group, using effective birth rates based on surviving infants (see Appendix A3)

Acronyms: CDC = (U.S.) Centers for Disease Control and Prevention; cVDPV = circulating vaccine-derived poliovirus; DEB = differential equation-based; FRPV = fully-reverted poliovirus; GPLN = Global Polio Laboratory Network; IPV = inactivated poliovirus vaccine; LPV = live poliovirus; OPV = oral poliovirus vaccine; PIR = paralysis-to-infection ratio; PV(1,2,3) = poliovirus (type 1, 2, or 3, respectively); R₀ = basic reproductive number; UN = United Nations; USA = United States of America; VAPP = vaccine-associated paralytic poliomyelitis; VP1 = viral protein 1; WPV(1,2,3) = wild poliovirus (type 1, 2, or 3, respectively)

Mean estimates obtained from experts and used in the model for the different immunity states, serotypes, and excretion modes vary between 2.85 and 3.37 days.