model {
   mu_10 ~ dnorm(-2.6,0.3)
   tau ~ dgamma(0.1,0.1)
   mu <- mu_10 *log(10)
   sigma <- 1/tau
   sigma_10 <- sigma/(log(10)*log(10))
#hepg control
   for (i in 1:N) {
     uc[i] ~ dlnorm(mu,tau)
     uc_ml[i] <- uc[i]*1/vc
     pc1[i] <- 1-exp(-1*uc[i])
     pc2[i] <- 1-exp(-0.2*uc[i])
     pc3[i] <- 1-exp(-0.1*uc[i])
     pcr_c[i,1] ~ dbin(pc1[i],5)
     pcr_c[i,2] ~ dbin(pc2[i],10)
     pcr_c[i,3] ~ dbin(pc3[i],10)
#hepg spike
     us[i] ~ dlnorm(mu,tau) 
     us_ml[i] <- us[i]*1/vs
     ps1[i] <- 1-exp(-1*us[i])
     ps2[i] <- 1-exp(-0.2*us[i])
     ps3[i] <- 1-exp(-0.1*us[i])
     pcr_s[i,1] ~ dbin(ps1[i],5)
     pcr_s[i,2] ~ dbin(ps2[i],10)
     pcr_s[i,3] ~ dbin(ps3[i],10)
     error[i] <- (uc[i] - us[i])/uc[i]
   }
#human virus
   for (i in 1:n) {
     u[i] ~ dlnorm(mu,tau)
	loss[i] ~ dbeta(50.75,5.25) 
     re[i] <- 1/(1-error[batch.index[i]])
     u_liter[i] <- (u[i]*(1/v)*f*re[i]*(1/(1-loss[i])))/pcr[i,13]
 
     p_1[i] <- 1-exp(-1*u[i])
     p_0.2[i] <- 1-exp(-0.2*u[i])
     p_0.1[i] <- 1-exp(-0.1*u[i])
     p_0.04[i] <- 1-exp(-0.04*u[i])
     p_0.03[i] <- 1-exp(-0.03125*u[i])
     p_0.02[i] <- 1-exp(-0.02*u[i])
   
     #likelihoods
     pcr[i,1] ~ dbin(p_1[i],pcr[i,7])
     pcr[i,2] ~ dbin(p_0.2[i],pcr[i,8])
     pcr[i,3] ~ dbin(p_0.1[i],pcr[i,9])
     pcr[i,4] ~ dbin(p_0.04[i],pcr[i,10])
     pcr[i,5] ~ dbin(p_0.03[i],pcr[i,11])
     pcr[i,6] ~ dbin(p_0.02[i],pcr[i,12])
   }

}
list(pcr_c=structure(.Data=c(
#1s
5,10,9,
#1t
5,10,9,
#2s
5,10,7,
#2t
5,10,7,
#3s(count 5 for batch index)			
5,6,1,

#3t(count 6 for batch index)	
5,10,4,
#4s(count 7 for batch index)
5,6,1,
#5s
5,9,6,
#10s(count 9 for batch index)
5,8,5,
#10t
5,9,6,

#11s(count 11 for batch index)
5,10,4,
#11t
5,10,5,
#12s
5,7,3,
#12t
5,7,3,
#13s
5,7,7,

#14s
5,10,5,
#15s
5,8,5,
#15t
5,9,5,
#16s
5,10,8,
#16t
5,10,8,

#17s
5,9,5,
#18s
5,10,9,
#18t
5,10,9,
#19s
5,7,7,
#20s
5,4,1,

#20t(count 26 for batch index)
5,9,7,
#21s
5,8,7,
#22s(count 28 for batch index)
5,9,7,
#23s(count 29 for batch index)
5,9,5,
#23t(count 30 for batch index)
5,9,5,

#24s(count 31 for batch index)
5,7,2,
#25s(count 32 for batch index)
5,10,3,
#25t(count 33 for batch index)
5,7,2,
#26s(count 34 for batch index)
5,10,3,
#27s(count 35 for batch index)
5,4,1,

#28s
5,8,7,
#29s
5,10,9
),.Dim=c(37,3)),vc=0.0045,N=37,
pcr_s=structure(.Data=c(
#1s
0,0,0,
#1t
0,0,0,
#2s
0,0,6,
#2t
5,10,8,
#3s
0,5,3,
#3t
0,8,9,
#4s
0,3,0,
#4t
#5s 
0,10,9,
#5t
#10s
0,8,8,
#10t
0,10,9,
#11s
0,6,3,
#11t
2,9,10,
#12s
0,9,7,
#12t
3,10,6,
#13s
0,0,2,
#13t
#14s
0,8,4,
#14t
#15s
0,4,2,
#15t
0,8,7,
#16s
0,0,0,
#16t
0,10,9,
#17s
0,2,6,
#17t
#18s
0,0,0,
#18t
0,10,9,
#19s
0,0,0,
#19t
#20s
0,0,1,
#20t
2,9,8,
#21s
0,3,1,
#21t
#22s
0,9,9,
#22t
#23s
0,10,6,
#23t
0,7,4,
#24s
0,7,5,
#24t
#25s
0,0,0,
#25t
0,7,4,
#26s
0,0,1,
#26t
#27s
0,0,0,
#27t
#28s
0,0,2,
#28t
#29s
0,4,2
#29t
),
.Dim=c(37,3)),N=37,vs=0.0045,pcr=structure(.Data=c(
#1s dec
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#1t dec
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,287.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,287.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,287.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,287.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,287.0,

#2s sept
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,208.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,208.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,208.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,208.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,208.9,
#2t sept
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2573.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2573.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2573.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2573.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2573.3,

#3s oct
0,2,NA,NA,4,NA,2,2,5,5,5,5,207.7,
0,6,NA,3,NA,NA,2,7,5,5,5,5,207.7,
2,7,7,1,1,NA,2,7,10,5,5,5,207.7,
2,2,5,5,1,0,2,2,5,5,5,5,207.7,
0,3,0,NA,NA,NA,2,7,5,5,5,5,207.7,
#3t oct
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2004.7,
0,3,NA,0,NA,NA,7,7,5,5,5,5,2004.7,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2004.7,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2004.7,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2004.7,

#4s oct
2,2,4,NA,NA,NA,2,2,5,5,5,5,200.2,
0,5,4,NA,NA,NA,2,7,5,5,5,5,200.2,
2,2,4,3,NA,NA,2,2,5,5,5,5,200.2,
0,7,5,4,NA,3,2,7,5,5,5,5,200.2,
0,4,NA,NA,NA,NA,2,7,5,5,5,5,200.2,

#no 4t oct
#5s mar
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.9,
#no 5t sample oct

#10s jan
#corrected number of reps fm 12 to 7
2,1,NA,NA,NA,NA,7,7,5,5,5,5,57.1,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,57.1,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,57.1,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,57.1,
0,1,NA,NA,NA,NA,2,7,5,5,5,5,57.1,
#10t jan
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2160.1,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2160.1,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2160.1,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2160.1,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2160.1,

#11s march
0,2,NA,NA,NA,NA,2,7,5,5,5,5,81.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,81.3,
0,4,NA,NA,NA,NA,2,7,5,5,5,5,81.3,
0,2,NA,2,NA,NA,7,2,5,5,5,5,81.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,81.3,
#11t march
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.0,

#12s feb
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,205.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,205.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,205.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,205.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,205.3,
#12t feb
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2002.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2002.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2002.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2002.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2002.2,

#13s may
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#13t no sample

#14s april
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,199.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,199.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,199.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,199.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,199.9,
#14t no sample april

#15s april
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,65.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,65.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,65.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,65.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,65.2,
#15t april
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.2,

#16S april
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,27.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,27.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,27.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,27.9,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,27.9,
#16t april
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,538.1,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,538.1,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,538.1,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,538.1,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,538.1,

#17s may
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,54.5,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,54.5,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,54.5,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,54.5,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,54.5,
#17t no samples may

#18s june
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,214.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,214.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,214.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,214.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,214.4,
#18t june
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,695.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,695.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,695.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,695.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,695.4,

#19s june
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,201.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,201.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,201.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,201.2,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,201.2,
#19t no samples june

#20s jan
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,35.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,35.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,35.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,35.3,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,35.3,
#20t jan
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2003.7,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2003.7,
1,0,NA,NA,NA,NA,7,2,5,5,5,5,2003.7,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2003.7,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2003.7,

#21s july
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.4,
#21t no samples july

#22S nov
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,144.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,144.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,144.4,
0,2,NA,NA,NA,NA,2,7,5,5,5,5,144.4,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,144.4,
#22t no samples nov

#23S aug
1,4,NA,NA,NA,NA,2,7,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,

#23t aug
2,2,1,NA,NA,NA,2,2,5,5,5,5,2000.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,2000.0,

#24s dec
2,0,NA,NA,NA,NA,7,2,5,5,5,5,1999.7,
0,2,NA,NA,NA,NA,7,7,5,5,5,5,1999.7,
2,0,NA,NA,NA,NA,7,2,5,5,5,5,1999.7,
0,1,NA,NA,NA,NA,2,7,5,5,5,5,1999.7,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,1999.7,
#24t no samples dec

#25s oct
0,0,NA,1,NA,NA,2,2,5,5,5,5,88.5,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,88.5,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,88.5,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,88.5,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,88.5,
#25t oct
5,1,NA,NA,NA,NA,7,7,5,5,5,5,673.5,
2,0,NA,NA,NA,NA,7,7,5,5,5,5,673.5,
1,4,1,NA,NA,NA,2,7,5,5,5,5,673.5,
2,3,1,NA,NA,NA,2,7,5,5,5,5,673.5,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,673.5,

#26s jan
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,206.5,
0,7,NA,9,4,3,2,7,5,10,5,5,206.5,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,206.5,
0,3,NA,NA,NA,NA,2,7,5,5,5,5,206.5,
0,1,NA,0,NA,NA,2,7,5,5,5,5,206.5,
#26t no samples jan

#27s feb
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
0,5,NA,3,NA,NA,2,5,5,5,5,5,200.0
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#27t no samples feb

#28s nov
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#28t no samples nov

#29s march
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0,
#0,0,NA,NA,NA,NA,2,2,5,5,5,5,200.0
#29t no samples
),
#accounts for per ml(ie, v) and ml of NA extract used (ie f)
.Dim=c(33,13)),n=33,v=0.005,f=3,batch.index=c(
5,5,5,5,5,
6,
7,7,7,7,7,
9,9,
11,11,11,
26,
28,
29,
30,
31,31,31,31,
32,
33,33,33,33,
34,34,34,
35
))