From: Impact of viral drift on vaccination dynamics and patterns of seasonal influenza
Parameter | Description | Value (range) |
---|---|---|
q _{ s },q _{ v },q _{ r } | Fraction of individuals receiving vaccination | 0 - 1 |
σ | Vaccine efficacy | 0.6 – 0.95 |
μ | Fraction of population vaccinated | Variable |
m _{1} | Number of seasons that the protection acquired from natural infection lasts | 2 - 8 seasons |
m _{2} | Number of seasons that the protection acquired from vaccination lasts | 2 - 4 seasons |
γ | Recovery rate from infection | 0.2 day ^{-1} |
ϵ _{ j } | Amplitude of seasonal fluctuation | 0.85 |
α | Age since last infection | Variable |
${\beta}_{s},{\beta}_{v}^{i}\left(t\right),{\beta}_{r}\left(a\right)$
i = 0, 1, ⋯, m _{2} - 1 | Baseline transmission rates of infection for susceptible, vaccinated, and recovered individuals, respectively | β _{ s } = 150/N year ^{-1} (N: total population size) |
${\overline{\beta}}_{v}\left(t\right),{\overline{\beta}}_{r}$ | Baseline transmission rates of infection for previously vaccinated and recovered individuals, respectively, who also received vaccine for the current season | Variable |
κ _{ s }(t) = β _{ s } · P _{ s }(t) | Transmission rate of infection for susceptible class | Variable |
${\kappa}_{v}^{0}\left(t\right)={\beta}_{v}^{0}\left(t\right){P}_{s}\left(t\right)$ | Transmission rate of infection for newly vaccinated from susceptible class | Variable |
${\kappa}_{v}^{i}\left(t\right)={\beta}_{v}^{i}\left(t\right){P}_{v}\left(t\right)$ | Transmission rate of infection for previously vaccinated individuals who received their last vaccine i seasons ago | Variable |
i = 1, 2, ⋯, m _{2} - 1 | ||
${\overline{\kappa}}_{v}\left(t\right)={\overline{\beta}}_{v}\xb7{P}_{v}\left(t\right)$ | Transmission rate of infection for previously vaccinated individuals who also received vaccine for the current season | Variable |
κ _{ r }(t, a) = β _{ r }(a) · P _{ r }(t) | Transmission rate of infection for recovered individuals with the recovery age α since last infection | Variable |
${\overline{\kappa}}_{r}\left(t\right)={\overline{\beta}}_{r}\xb7{P}_{r}\left(t\right)$ | Transmission rate of infection for recovered individuals who received vaccine for the current season | Variable |