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Table 1 Summary of the models considered for each of the pathogens and the corresponding model parameter estimates using the observed serological survey data

From: Sample size calculation for estimating key epidemiological parameters using serological data and mathematical modelling

Serological data Models Estimates
Measles Logistic model with piecewise constant prevalence \( {\widehat{\beta}}_{Measles}=\left(0.108,1.733,1.412,1.819,2.479,3.863\right) \)
Mumps Logistic model with piecewise constant prevalence \( {\widehat{\beta}}_{Mumps}=\left(-0.575,1.317,1.990,1.950,2.145,2.112\right) \)
Rubella Logistic model with piecewise constant prevalence \( {\widehat{\beta}}_{Rub}=\left(0.050,1.912,2.356,2.419,3.099,3.339\right) \)
VZV MSIR piecewise constant force of infection \( {\widehat{\lambda}}_{VZV}=\left(\mathrm{0.330,0.301,0.245,0},\mathrm{0.071,0.116}\right) \)
Exponentially damped model for force of infection \( {\widehat{\alpha}}_{VZV}=\left(\mathrm{0.476,0.468,0.071}\right) \)
Parvovirus B19 MSIR piecewise constant force of infection \( {\widehat{\lambda}}_{B19}=\left(\mathrm{0.065,0.086,0.114,0.036,0},0.014\right) \)
Exponentially damped model for force of infection \( {\widehat{\alpha}}_{B19}=\left(\mathrm{0.076,0.241,0.006}\right) \)
MSIR model with boosting and waning (MSIRWb-ext AW) \( \widehat{q}=0.085 \), \( {\widehat{\varepsilon}}_1=0.012 \), \( {\widehat{\varepsilon}}_2=0 \), and \( \widehat{\varphi}=0.334 \).
  1. VZV varicella-zoster virus, MSIR model Maternally-derived immunity-Susceptible-Infectious-Recovered model. \( \widehat{\beta} \): coefficient estimates (logit scale) within the age classes [1,2), [2,11), [11,16), [16,21), [21,31), and [31,65] years. \( \widehat{\lambda} \): estimates of the force of infection within the age classes [1,2), [2,6), [6,12), [12,19), [19,31), and [31,65] years. \( \widehat{\alpha} \): estimates of the three parameters describing the exponentially damped model. \( \widehat{q} \): estimated proportionality factor between the transmission and contact rates; \( \widehat{\varepsilon_1} \) and \( \widehat{\varepsilon_2} \): estimated rates at which individuals moved from the high immunity state R to the low immunity state W for age group < 35 and ≥ 35 years respectively; φ: estimated proportionality factor between the boosting rate and the force of infection. See the Models section for more details