Table 1.

Polio Transmission Model Parameters

Model Parameters	Descriptions	Values
i	Waning stage	1 … n
j	Age group	1 … m
n	Total immune stages	10
m	Total age groups	34
b	Birth rate into population	0.025a
c	Effective contact rate	40–200/yearb
βi	Relative susceptibility for immune stage, i	0–1c,d
θi	Relative contagiousness for immune stage, i	0–1c,e
γi	Recovery rate for immune stage, i	10–40/yearc,f
ωi	Rate of immune state change	0, 0.2, or 2/yearg
φj	Effective vaccination rate	0–3/year
ε	Relative contagiousness OPV:WPV	0.15–0.45h
κ	Relative recovery rate OPV:WPV	2.25–6.25h
μj	Age-dependent death rates	−i

Abbreviations: OPV, oral polio vaccine; WPV, wild poliovirus.

^a The birth rate, b, was set in relation to the death rate, μ_j, so that the population size is constant.

^b The effective contact rate, c, was assigned by using previously established R₀ values (26), along with our derived transmission model calculation of R₀ (Table 2).

^c Immunity responses to susceptibility, contagiousness, and duration of contagiousness were assigned across their ranges of values by using an exponential function (see Web Appendix 4.1 for more details).

^d The immunity parameter for susceptibility, β_i, attenuates the infectivity of an effective contact on the susceptible population, where 1 defines no reduction (no immunity) and 0 defines no susceptibility (full immunity).

^e The measure of contagiousness, θ_i, attenuates the force of infection due to the infected population, where 1 defines full contagiousness (no immunity) and 0 defines no contagiousness (full immunity).

^f The recovery rate, γ_i is defined according to observed ranges of shedding duration (24, 25).

^g See Web Appendix 4.2 and Web Table 1.

^h We attenuate the effect of OPV transmission by reducing contagiousness and duration of illness by using parameters ɛ and κ, respectively. The κ value was set relatively to ɛ, and values were determined by using sensitivity analysis and known relative transmissibility of OPV (26).

ⁱ −, refer to Web Appendix 3.