{

  #model specification

  for (i in 1:observations) {

    #app_p:apparent prevalence

    y[i] ~ dbin(app_p[i], n[i])

    #animal_p: animal prevalence

    #Se:sensitivity

    #Sp:specificity

    app_p[i] <- animal_p[i] * Seser + (1 - animal_p[i]) * (1 - Spser)


    #animal_lev_p: animal level prevalence

    #herd_not_free: (0/1) the herd is free or not

    animal_p[i] <- animal_lev_p[i] * herd_not_free[i]

    herd_not_free[i] ~ dbern(herd_p[region[i]])

    animal_lev_p[i] ~ dbeta(alpha, beta)


    #a: indices to calculate disease freedom or disease exceeding a prespecified level (here 9.5%) for the animals within each herd.

    a[1, i] <- equals(animal_p[i], 0)

    a[2, i] <- step(0.095-animal_p[i])

  }

  for (j in 1:regions) {

    #herd_p: herd prevalence

    #herd_lev_p: herd level prevalence

    #region_not_free: (0/1) the region is free or not 

    herd_p[j] <- herd_lev_p[j] * region_not_free[j]

   # herd_lev_p[j] ~ dbeta(ahp, bhp)
 herd_lev_p[j] ~ dbeta(1, 1)
  

    #region_p: region prevalence

    region_not_free[j] ~ dbern(region_p)

    

    #b: indices to calculate disease freedom or disease exceeding a prespecified level (here 50%) for the herds within each region.

    b[1, j] <- equals(herd_p[j], 0)

    b[2, j] <- step(0.50 - herd_p[j])

  }

  

  #region_p ~ dbeta(arp, brp)    
region_p ~ dbeta(1, 1) 

  

  #c: indices to calculate disease freedom or disease exceeding a prespecified level (here 50%) for the regions within the country.

  c[1] <- equals(region_p, 0)

  c[2] <- step(0.5 - region_p)

  

  #priors

  #mu: mean prevalence in infected herds

  #psi: a parameter expressing the variability of prevalence among infected herds 

  mu ~ dbeta(amu, bmu)

  psi ~ dgamma(apsi, bpsi)

  alpha <- mu * psi

  beta <- psi * (1 - mu)

  Se1 ~ dbeta(ase1, bse1)

  Sp1 ~ dbeta(asp1, bsp1)

  

  Se2 ~ dbeta(ase2, bse2)

  Sp2 ~ dbeta(asp2, bsp2)

Spser<-1-(1-Sp1)*(1-Sp2)

    Seser<-Se1*Se2

}



##Data

list(region=c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4	,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7	,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8	,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10),y=c(6,0,1,0,0,1,1,0,0,4,0,0,1,1,0,0,1,0,0,4,0,	0,0,0,0,0,0,3,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,	0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0),n=c(15,2,2,2,2,2,2,2,1,15,2,1,2,2,2,2,2,1,1,15,3,3,2,2,2,2,1,15,2,2,2,2,2,2,1,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,1,2,1,1,2,2,2,2,2,2,2,22,2,1,1,1,2,2,2,1,15,2,1,1,1,2,2,2,2,2,9,2,2,2,2,2,2,2,2,2,2,10,1,1,1,2,2,2,2,2,1,2,2,2,50,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,10,2,2,2,2,2,2,2,2,2,2,10,2,2,2,1,3,3,1,2,2,2),observations=189,regions=10,ase1=7.99,bse1=2.75,asp1=8.3045,bsp1=1.81, ase2=73.81,bse2=65.57,asp2=176.39,bsp2=6.42,amu=3.82,bmu=36.43,apsi=7.55,bpsi=1.42)