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Table 4 List of the model stochastic transitions and their rates

From: The role of hand hygiene in controlling norovirus spread in nursing homes

Events

Transitions

Rates

1- Resident admission to the NH

S R  → S R  + 1

μ × N R

2- Susceptible resident discharge out of the NH (or death)

S R  → S R  − 1

μ × S R

3- Susceptible resident exposed to the virus

S R  → S R  − 1 & E R  → E R  + 1

R  = p × [(1-h RR ) × C RR ×(I R  + α × E R  + α × A R ) + (1-h SR ) × C SR ×(I S  + α × E S  + α × A S )]

4- Exposed resident discharge out of the NH (or death)

E R  → E R -1

μ × E R

5- Start of symptoms in exposed residents

E R  → E R -1 & I R  → I R  + 1

 × E R

6- Infected symptomatic resident discharge out of the NH (or death)

I R  → I R -1

μ × I R

7- Asymptomatic resident discharge out of the NH (or death)

A R  → A R -1

μ × A R

8- End of symptoms in residents

I R  → I R -1 & A R  → A R  + 1

σ × I R

9- Recovery of an asymptomatic resident

A R  → A R -1 & R R  → R R  + 1

ρ × A R

10- Recovered resident discharge out of the NH (or death)

R R  → R R -1

μ × R R

11- Immunity loss of a resident

R R  → R R -1 & S R  → S R  + 1

θ × R R

12- Susceptible staff member exposed to the virus

S S  → S S -1 & E S  → E S  + 1

S  = p × [(1-h SS ) × C SS ×(I S  + α × E S  + α × A S ) + (1-h SR ) × C SR ×(I R  + α × E R  + α × A R )]

13- Start of symptoms in exposed staff members

Ep → E S -1 & Ip → I S  + 1

 × E S

14- End of symptoms in staff members

I S  → I S -1 & A S  → A S  + 1

σ × I S

15- Recovery of an asymptomatic staff member

A S  → A S -1 & R S  → R S  + 1

ρ × A S

16- Immunity loss of a staff member

R S  → R S -1 & S S  → S S  + 1

θ × R S

  1. S R and S S respectively number of susceptible residents and staff members
  2. E R and E S respectively number of exposed residents and staff members
  3. I R and I S respectively number of infected symptomatic residents and staff members
  4. A R and A S respectively number of asymptomatic residents and staff members
  5. R R and R S respectively number of recovered residents and staff members
  6. μ admission and discharge rate
  7. p per-contact probability of transmission
  8. C RR contact rate resident-resident
  9. C SR contact rate staff-resident
  10. C SS contact rate staff-staff
  11. h RR hand hygiene compliance rate during resident-resident interactions
  12. h SR hand hygiene compliance rate during staff-resident interactions
  13. h SS hand hygiene compliance rate during staff-staff interactions
  14. α Relative infectiousness of A and E individuals
  15. 1/ Duration of incubation
  16. 1/σ Duration of symptoms
  17. ρ Recovery rate
  18. θ Rate of immunity loss