model{

for (i in 1:3) {
    for (j in 1:229) {
        Data_Serology[i,j] ~ dbern(p_Serology[i,j])
        p_Serology[i,j] <- (1-Spec_Serology) * (1-PosYN_Final[i,j]) + PosYN_Final[i,j]*Sens_Serology
        PosYN_Serology[i,j] ~ dbern(p_Serology[i,j]) 

        Data_Culture[i,j] ~ dbern(p_Culture[i,j])
        p_Culture[i,j] <- (1-Spec_Culture) * (1-PosYN_Final[i,j]) + PosYN_Final[i,j]*Sens_Culture
        PosYN_Culture[i,j] ~ dbern(p_Culture[i,j]) 

    PosYN_Final[i,j] ~ dbern(p_Pos[i,j])
    
    p_PosFinal[i,j] <- (Incidence[i]  * Utilisation * Ep * N[i,j] * D/365)/(Et[i,j] * 100000)
    p_Pos[i,j] <- max(0.0001, min(0.9999, p_PosFinal[i,j])) 

    }
}

    Utilisation ~dbeta(5.792023, 23.42362)   

    # Priors 
    Sens_Culture ~ dbeta(2.093424, 2.093424)
    Spec_Culture <- 1
    Sens_Serology ~ dbeta(76.48972, 9.261087)
    Spec_Serology ~ dbeta(71.79824, 3.304522)

  
    for (i in 1:3) {
         Incidence[i] ~ dgamma(1.2, 0.002)
    }
    
  Ep <- 0.54
  D <- 259

}