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Table 1 Transition probabilities

From: Health economic evaluation of vaccination strategies for the prevention of herpes zoster and postherpetic neuralgia in Germany

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.