Fig 1.
Flow diagram of the compartmental model for VZV transmission and reactivation.
Boxes denotes epidemiological compartments (M = maternal antibody, S = susceptible to varicella infection, I = varicella infective, HZS1 = first time zoster susceptible, etc.), while arrows denote transfers between compartments; ω(a) denotes the rate of loss of maternal antibodies, λ(a) the varicella force of infection (FOI), γ the varicella recovery rate, (h = 1,2,3…) the force of exogenous boosting (FOB), and ρi(a) (i = 1,2,3…) the rates of HZ development in each HZ susceptibility stage.
Table 1.
The different hypotheses about the VZV reactivation rate.
Table 2.
Summary results for ML estimation of MSIR transmission models.
Fig 2.
The natural history of VZV in Norway: Fit to seroprevalence data and force of infection.
Top row: results from model Q3,16 based on the synthetic matrix; bottom row: results from model Q0 based on the Polymod matrix of close contacts. Left: predicted vs observed varicella age-specific sero-prevalence, with 95% confidence bands. Center: predicted age-specific varicella FOI with 95% confidence bands. Right: best R0 estimate, related distribution of bootstrap estimates and 95% percentile CI. For sake of comparison between models based on synthetic matrices (based on census data, and therefore lacking an uncertainty evaluation) vs models based on Polymod matrices (based on survey data), the bootstrap was done by re-sampling sero-prevalence data only.
Table 3.
Predicted age-specific varicella incidence.
Table 4.
ML estimation of the reactivation risk: The full-boosting case (z = 1).
Fig 3.
The natural history of VZV in Norway: Fit to age-specific HZ incidence by some models for VZV reactivation (Table 1) under the full boosting hypothesis (z = 1).
Top-left: the “duration since exposure” model; top-right: the Gompertz age-dependent model; bottom-left: the baseline model; bottom-right: the progressive immunity model. The underlying transmission model is based on the synthetic matrix, hypothesis Q3, 16. HZ incidence is represented per 1000 population, per year.
Fig 4.
The natural history of VZV in Norway.
Pattern of the AIC for some alternative models for the reactivation risk, for different levels of the boosting constant z. The underlying transmission model (Table 2) is based on the synthetic matrix, hypothesis Q3, 16.
Table 5.
Reproduction numbers of boosting.