# Table 1 Transition probabilities

State (From state → To state) Variable Formula
Death
Death → Death λi =1
Any state → Death αi = $p i Background Mortality$
Status quo [no vaccination]
Healthy
Healthy → Herpes zoster βi = $1 - α i ∗ 1 - e - I i Healthy → HZ$
Healthy → Healthy γi = 1 - α i - β i
Herpes zoster
Herpes Zoster → Death δi = $1 - α i ∗ 1 - e - I i HZ → Death$
Herpes Zoster → PHN ϵi = $1 - α i ∗ 1 - e - I i HZ → PHN$
Herpes Zoster → Healthy after disease ζi =  1 - α i - δ i - ϵi
PHN
PHN → PHN ηi = $χ 1 , D PHN σ ∗ 1 - α i$
PHN → Healthy after disease θi = 1 - α i - ηi
Healthy after disease
Healthy after disease → Healthy after disease κi = $χ 1 , D Rec σ ∗ 1 - α i + χ D Rec , ∞ σ ∗ γ i$
Healthy after disease → Herpes zoster ιi = 1 - α i - κ i
Vaccine-Scenario [adapted transition probability due to vaccine efficacy (VE)]
Healthy
Healthy → Herpes zoster βi V = $β i ∗ 1 - VE i HZ$
VEi HZ = $χ j , μ i ∗ IVE j HZ + χ μ , ∞ i ∗ IVE j HZ ∗ e - π * i - μ$
Healthy → Healthy γi V = $1 - α i - β i V$
HZ
Herpes zoster → PHN ϵi V = $ϵ i ∗ 1 - VE i PHN$
VEi PHN = $χ j , μ i ∗ IVE j PHN + χ μ , ∞ i ∗ IVE j PHN ∗ e - π * i - μ$
Healthy after disease
Healthy after Disease → Healthy after disease κi V = $χ 1 , D Rec σ ∗ 1 - α i + χ D Rec , ∞ σ ∗ γ i V$
Healthy after Disease → Herpes zoster ιi V = $1 - α i - κ i V$
1. p = probability of death with respect to cycle-length; i = age = Start_Age +(n_cycles); χ A(x) = Indicator function; σ = Tunnel (counter for cycles staying in state); DPHN = Duration of PHN; DRec = Duration until Recurrence is possible; v = indicating the vaccine scenario; j = Age at Vaccination; μ = Age at Vaccination plus n years; I = Age-group specific Incidencefrom_state→to_state with respect to cycle-length; VEi HZ = Vaccine efficacy protecting against HZ; IVEj HZ = Initial Vaccine efficacy protecting against HZ by age at vaccination; VEi PHN = Vaccine efficacy protecting against PHN by certain age in model; IVEj PHN = Initial Vaccine efficacy protecting against PHN by age at vaccination; π = Waning rate with respect to cycle-length.