ADM Task 4

max.ts = 15
delta = 1
startproxel=c(1,0,0,1,0)
RG=matrix(c(1,1,0,1,
            0,1,1,1,
            0,0,1,1,
            0,0,0,1),ncol = 4,byrow = T)

Proxel_algo=function(RG,startproxel,delta,max.ts,Print=T){
  
counter_prob=0

unihrf <- function(age, a, b) {
  if (a <= age && age < b) {
    return (1.0 / (b - age))
  } else {
    return (0)
  }
}

exphrf <- function(age, l) {
  return (l)
}
  
proxel_list=list()
proxel_list[[max.ts+1]]=list()
proxel_list[[1]]=list(STEP=c(0),proxel=data.frame(state=startproxel[1],tau=startproxel[2],tau_k=startproxel[3],prob=startproxel[4],prev=startproxel[5]))
if(Print) print("initial proxel:")
if(Print) print(proxel_list[[1]])

for (timestep in 1:max.ts) {
  proxel_list[[timestep+1]]=list(timestep=c(timestep),proxel=data.frame(state=numeric(),tau=numeric(),tau_k=numeric(),prob=numeric(),prev=numeric()))     # erstelle schonmal eine neue leere liste für den nächsten timestep
  
  for (l in 1:nrow(proxel_list[[timestep]]$proxel)) {
    currprox = proxel_list[[timestep]]$proxel[l,]                                     # aktueller proxel zu dem folgeproxels erzeugt werden sollen
    folger = RG[as.numeric(currprox[1]),]                                             # folgestates von aktuellem proxel
    
    for (i in 1:4) {
      if (folger[i]==1) {                                                             # erstelle folgeproxel falls pfeil dahin gibt
        proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel)+1,1] = i                       # state vom nächsten proxel
        
        if(currprox$state==i) proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),2] = currprox$tau + delta
          else proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),2] = 0                    # tau vom nächsten proxel
        
        if(currprox$state %in% c(1,2,3) & i!=4) proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),3] = currprox$tau_k + delta
          else if(currprox$state==4 & i==4) proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),3] = currprox$tau_k - delta
            else proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),3] = 0                   # tau_k vom nächsten proxel
          
        if(currprox$state==1 & i==2) {
          proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),4] = (unihrf(currprox$tau_k,2,4) * delta) * currprox$prob
          counter_prob = counter_prob + unihrf(currprox$tau_k,2,4) * delta}                 # transition von S1 zu S2
        if(currprox$state==2 & i==3) {
          proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),4] = (exphrf(currprox$tau_k,0.1) * delta) * currprox$prob
          counter_prob = counter_prob + exphrf(currprox$tau_k,0.1) * delta}                 # transition von S2 zu S3
        if(currprox$state!=4 & i==4) {
          proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),4] = (unihrf(currprox$tau_k,7,14)* delta) * currprox$prob
          counter_prob = counter_prob + unihrf(currprox$tau_k,7,14)* delta}                 # transtion zu heal von S1,S2 oder S3
        if(currprox$state==1 & i==1) {
          proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),4] = (1 - (unihrf(currprox$tau_k,2,4) * delta) - (unihrf(currprox$tau_k,7,14)* delta)) * currprox$prob}
        if(currprox$state==2 & i==2) {
          proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),4] = (1 - (exphrf(currprox$tau_k,0.1) * delta) - (unihrf(currprox$tau_k,7,14)* delta)) * currprox$prob}
        if(currprox$state==3 & i==3) {
          proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),4] = (1 - (unihrf(currprox$tau_k,7,14)* delta)) * currprox$prob}
        if(currprox$state==4 & i==4) {
          proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),4] = 1 }
            
         proxel_list[[timestep+1]]$proxel[nrow(proxel_list[[timestep+1]]$proxel),5] = l   
            
      }
    } 
    
    #proxel_list[[timestep+1]]$proxel[which(is.na(proxel_list[[timestep+1]]$proxel[,4])),4] = 1-counter_prob #* proxel_list[[timestep]]$proxel$prob[l] # rest wkt im state zu bleiben
    counter_prob=0
  }
  if(length(which(proxel_list[[timestep+1]]$proxel[,4]<=0))!=0) proxel_list[[timestep+1]]$proxel=proxel_list[[timestep+1]]$proxel[-which(proxel_list[[timestep+1]]$proxel[,4]<=0),]
  if(length(which(proxel_list[[timestep+1]]$proxel[,3]< 0))!=0) proxel_list[[timestep+1]]$proxel=proxel_list[[timestep+1]]$proxel[-which(proxel_list[[timestep+1]]$proxel[,3]< 0),]
  
  if(Print) print(paste("Time step:",timestep))
  if(Print) print(proxel_list[[timestep+1]])
}

return(proxel_list)
}
proxel_list=Proxel_algo(RG,startproxel,delta,max.ts,T)

## [1] "initial proxel:"
## $STEP
## [1] 0
## 
## $proxel
##   state tau tau_k prob prev
## 1     1   0     0    1    0
## 
## [1] "Time step: 1"
## $timestep
## [1] 1
## 
## $proxel
##   state tau tau_k prob prev
## 1     1   1     1    1    1
## 
## [1] "Time step: 2"
## $timestep
## [1] 2
## 
## $proxel
##   state tau tau_k prob prev
## 1     1   2     2    1    1
## 
## [1] "Time step: 3"
## $timestep
## [1] 3
## 
## $proxel
##   state tau tau_k prob prev
## 1     1   3     3  0.5    1
## 2     2   0     3  0.5    1
## 
## [1] "Time step: 4"
## $timestep
## [1] 4
## 
## $proxel
##   state tau tau_k prob prev
## 2     2   0     4 0.50    1
## 4     2   1     4 0.45    2
## 5     3   0     4 0.05    2
## 
## [1] "Time step: 5"
## $timestep
## [1] 5
## 
## $proxel
##   state tau tau_k  prob prev
## 1     2   1     5 0.450    1
## 2     3   0     5 0.050    1
## 4     2   2     5 0.405    2
## 5     3   0     5 0.045    2
## 7     3   1     5 0.050    3
## 
## [1] "Time step: 6"
## $timestep
## [1] 6
## 
## $proxel
##    state tau tau_k   prob prev
## 1      2   2     6 0.4050    1
## 2      3   0     6 0.0450    1
## 4      3   1     6 0.0500    2
## 6      2   3     6 0.3645    3
## 7      3   0     6 0.0405    3
## 9      3   1     6 0.0450    4
## 11     3   2     6 0.0500    5
## 
## [1] "Time step: 7"
## $timestep
## [1] 7
## 
## $proxel
##    state tau tau_k    prob prev
## 1      2   3     7 0.36450    1
## 2      3   0     7 0.04050    1
## 4      3   1     7 0.04500    2
## 6      3   2     7 0.05000    3
## 8      2   4     7 0.32805    4
## 9      3   0     7 0.03645    4
## 11     3   1     7 0.04050    5
## 13     3   2     7 0.04500    6
## 15     3   3     7 0.05000    7
## 
## [1] "Time step: 8"
## $timestep
## [1] 8
## 
## $proxel
##    state tau tau_k        prob prev
## 1      2   4     8 0.275978571    1
## 2      3   0     8 0.036450000    1
## 3      4   0     0 0.052071429    1
## 4      3   1     8 0.034714286    2
## 5      4   0     0 0.005785714    2
## 6      3   2     8 0.038571429    3
## 7      4   0     0 0.006428571    3
## 8      3   3     8 0.042857143    4
## 9      4   0     0 0.007142857    4
## 10     2   5     8 0.248380714    5
## 11     3   0     8 0.032805000    5
## 12     4   0     0 0.046864286    5
## 13     3   1     8 0.031242857    6
## 14     4   0     0 0.005207143    6
## 15     3   2     8 0.034714286    7
## 16     4   0     0 0.005785714    7
## 17     3   3     8 0.038571429    8
## 18     4   0     0 0.006428571    8
## 19     3   4     8 0.042857143    9
## 20     4   0     0 0.007142857    9
## 
## [1] "Time step: 9"
## $timestep
## [1] 9
## 
## $proxel
##    state tau tau_k        prob prev
## 1      2   5     9 0.202384286    1
## 2      3   0     9 0.027597857    1
## 3      4   0     0 0.045996429    1
## 4      3   1     9 0.030375000    2
## 5      4   0     0 0.006075000    2
## 7      3   2     9 0.028928571    4
## 8      4   0     0 0.005785714    4
## 10     3   3     9 0.032142857    6
## 11     4   0     0 0.006428571    6
## 13     3   4     9 0.035714286    8
## 14     4   0     0 0.007142857    8
## 16     2   6     9 0.182145857   10
## 17     3   0     9 0.024838071   10
## 18     4   0     0 0.041396786   10
## 19     3   1     9 0.027337500   11
## 20     4   0     0 0.005467500   11
## 22     3   2     9 0.026035714   13
## 23     4   0     0 0.005207143   13
## 25     3   3     9 0.028928571   15
## 26     4   0     0 0.005785714   15
## 28     3   4     9 0.032142857   17
## 29     4   0     0 0.006428571   17
## 31     3   5     9 0.035714286   19
## 32     4   0     0 0.007142857   19
## 
## [1] "Time step: 10"
## $timestep
## [1] 10
## 
## $proxel
##    state tau tau_k        prob prev
## 1      2   6    10 0.141669000    1
## 2      3   0    10 0.020238429    1
## 3      4   0     0 0.040476857    1
## 4      3   1    10 0.022078286    2
## 5      4   0     0 0.005519571    2
## 7      3   2    10 0.024300000    4
## 8      4   0     0 0.006075000    4
## 10     3   3    10 0.023142857    6
## 11     4   0     0 0.005785714    6
## 13     3   4    10 0.025714286    8
## 14     4   0     0 0.006428571    8
## 16     3   5    10 0.028571429   10
## 17     4   0     0 0.007142857   10
## 19     2   7    10 0.127502100   12
## 20     3   0    10 0.018214586   12
## 21     4   0     0 0.036429171   12
## 22     3   1    10 0.019870457   13
## 23     4   0     0 0.004967614   13
## 25     3   2    10 0.021870000   15
## 26     4   0     0 0.005467500   15
## 28     3   3    10 0.020828571   17
## 29     4   0     0 0.005207143   17
## 31     3   4    10 0.023142857   19
## 32     4   0     0 0.005785714   19
## 34     3   5    10 0.025714286   21
## 35     4   0     0 0.006428571   21
## 37     3   6    10 0.028571429   23
## 38     4   0     0 0.007142857   23
## 
## [1] "Time step: 11"
## $timestep
## [1] 11
## 
## $proxel
##    state tau tau_k        prob prev
## 1      2   7    11 0.092084850    1
## 2      3   0    11 0.014166900    1
## 3      4   0     0 0.035417250    1
## 4      3   1    11 0.015178821    2
## 5      4   0     0 0.005059607    2
## 7      3   2    11 0.016558714    4
## 8      4   0     0 0.005519571    4
## 10     3   3    11 0.018225000    6
## 11     4   0     0 0.006075000    6
## 13     3   4    11 0.017357143    8
## 14     4   0     0 0.005785714    8
## 16     3   5    11 0.019285714   10
## 17     4   0     0 0.006428571   10
## 19     3   6    11 0.021428571   12
## 20     4   0     0 0.007142857   12
## 22     2   8    11 0.082876365   14
## 23     3   0    11 0.012750210   14
## 24     4   0     0 0.031875525   14
## 25     3   1    11 0.013660939   15
## 26     4   0     0 0.004553646   15
## 28     3   2    11 0.014902843   17
## 29     4   0     0 0.004967614   17
## 31     3   3    11 0.016402500   19
## 32     4   0     0 0.005467500   19
## 34     3   4    11 0.015621429   21
## 35     4   0     0 0.005207143   21
## 37     3   5    11 0.017357143   23
## 38     4   0     0 0.005785714   23
## 40     3   6    11 0.019285714   25
## 41     4   0     0 0.006428571   25
## 43     3   7    11 0.021428571   27
## 44     4   0     0 0.007142857   27
## 
## [1] "Time step: 12"
## $timestep
## [1] 12
## 
## $proxel
##    state tau tau_k        prob prev
## 1      2   8    12 0.052181415    1
## 2      3   0    12 0.009208485    1
## 3      4   0     0 0.030694950    1
## 4      3   1    12 0.009444600    2
## 5      4   0     0 0.004722300    2
## 7      3   2    12 0.010119214    4
## 8      4   0     0 0.005059607    4
## 10     3   3    12 0.011039143    6
## 11     4   0     0 0.005519571    6
## 13     3   4    12 0.012150000    8
## 14     4   0     0 0.006075000    8
## 16     3   5    12 0.011571429   10
## 17     4   0     0 0.005785714   10
## 19     3   6    12 0.012857143   12
## 20     4   0     0 0.006428571   12
## 22     3   7    12 0.014285714   14
## 23     4   0     0 0.007142857   14
## 25     2   9    12 0.046963274   16
## 26     3   0    12 0.008287637   16
## 27     4   0     0 0.027625455   16
## 28     3   1    12 0.008500140   17
## 29     4   0     0 0.004250070   17
## 31     3   2    12 0.009107293   19
## 32     4   0     0 0.004553646   19
## 34     3   3    12 0.009935229   21
## 35     4   0     0 0.004967614   21
## 37     3   4    12 0.010935000   23
## 38     4   0     0 0.005467500   23
## 40     3   5    12 0.010414286   25
## 41     4   0     0 0.005207143   25
## 43     3   6    12 0.011571429   27
## 44     4   0     0 0.005785714   27
## 46     3   7    12 0.012857143   29
## 47     4   0     0 0.006428571   29
## 49     3   8    12 0.014285714   31
## 50     4   0     0 0.007142857   31
## 
## [1] "Time step: 13"
## $timestep
## [1] 13
## 
## $proxel
##    state tau tau_k        prob prev
## 1      2   9    13 0.020872566    1
## 2      3   0    13 0.005218142    1
## 3      4   0     0 0.026090708    1
## 4      3   1    13 0.004604243    2
## 5      4   0     0 0.004604243    2
## 7      3   2    13 0.004722300    4
## 8      4   0     0 0.004722300    4
## 10     3   3    13 0.005059607    6
## 11     4   0     0 0.005059607    6
## 13     3   4    13 0.005519571    8
## 14     4   0     0 0.005519571    8
## 16     3   5    13 0.006075000   10
## 17     4   0     0 0.006075000   10
## 19     3   6    13 0.005785714   12
## 20     4   0     0 0.005785714   12
## 22     3   7    13 0.006428571   14
## 23     4   0     0 0.006428571   14
## 25     3   8    13 0.007142857   16
## 26     4   0     0 0.007142857   16
## 28     2  10    13 0.018785309   18
## 29     3   0    13 0.004696327   18
## 30     4   0     0 0.023481637   18
## 31     3   1    13 0.004143818   19
## 32     4   0     0 0.004143818   19
## 34     3   2    13 0.004250070   21
## 35     4   0     0 0.004250070   21
## 37     3   3    13 0.004553646   23
## 38     4   0     0 0.004553646   23
## 40     3   4    13 0.004967614   25
## 41     4   0     0 0.004967614   25
## 43     3   5    13 0.005467500   27
## 44     4   0     0 0.005467500   27
## 46     3   6    13 0.005207143   29
## 47     4   0     0 0.005207143   29
## 49     3   7    13 0.005785714   31
## 50     4   0     0 0.005785714   31
## 52     3   8    13 0.006428571   33
## 53     4   0     0 0.006428571   33
## 55     3   9    13 0.007142857   35
## 56     4   0     0 0.007142857   35
## 
## [1] "Time step: 14"
## $timestep
## [1] 14
## 
## $proxel
##    state tau tau_k        prob prev
## 2      3   0    14 0.002087257    1
## 3      4   0     0 0.020872566    1
## 5      4   0     0 0.005218142    2
## 8      4   0     0 0.004604243    4
## 11     4   0     0 0.004722300    6
## 14     4   0     0 0.005059607    8
## 17     4   0     0 0.005519571   10
## 20     4   0     0 0.006075000   12
## 23     4   0     0 0.005785714   14
## 26     4   0     0 0.006428571   16
## 29     4   0     0 0.007142857   18
## 32     3   0    14 0.001878531   20
## 33     4   0     0 0.018785309   20
## 35     4   0     0 0.004696327   21
## 38     4   0     0 0.004143818   23
## 41     4   0     0 0.004250070   25
## 44     4   0     0 0.004553646   27
## 47     4   0     0 0.004967614   29
## 50     4   0     0 0.005467500   31
## 53     4   0     0 0.005207143   33
## 56     4   0     0 0.005785714   35
## 59     4   0     0 0.006428571   37
## 62     4   0     0 0.007142857   39
## 
## [1] "Time step: 15"
## $timestep
## [1] 15
## 
## $proxel
##    state tau tau_k        prob prev
## 1      3   1    15 0.002087257    1
## 13     3   1    15 0.001878531   12

proxel_list

## [[1]]
## [[1]]$STEP
## [1] 0
## 
## [[1]]$proxel
##   state tau tau_k prob prev
## 1     1   0     0    1    0
## 
## 
## [[2]]
## [[2]]$timestep
## [1] 1
## 
## [[2]]$proxel
##   state tau tau_k prob prev
## 1     1   1     1    1    1
## 
## 
## [[3]]
## [[3]]$timestep
## [1] 2
## 
## [[3]]$proxel
##   state tau tau_k prob prev
## 1     1   2     2    1    1
## 
## 
## [[4]]
## [[4]]$timestep
## [1] 3
## 
## [[4]]$proxel
##   state tau tau_k prob prev
## 1     1   3     3  0.5    1
## 2     2   0     3  0.5    1
## 
## 
## [[5]]
## [[5]]$timestep
## [1] 4
## 
## [[5]]$proxel
##   state tau tau_k prob prev
## 2     2   0     4 0.50    1
## 4     2   1     4 0.45    2
## 5     3   0     4 0.05    2
## 
## 
## [[6]]
## [[6]]$timestep
## [1] 5
## 
## [[6]]$proxel
##   state tau tau_k  prob prev
## 1     2   1     5 0.450    1
## 2     3   0     5 0.050    1
## 4     2   2     5 0.405    2
## 5     3   0     5 0.045    2
## 7     3   1     5 0.050    3
## 
## 
## [[7]]
## [[7]]$timestep
## [1] 6
## 
## [[7]]$proxel
##    state tau tau_k   prob prev
## 1      2   2     6 0.4050    1
## 2      3   0     6 0.0450    1
## 4      3   1     6 0.0500    2
## 6      2   3     6 0.3645    3
## 7      3   0     6 0.0405    3
## 9      3   1     6 0.0450    4
## 11     3   2     6 0.0500    5
## 
## 
## [[8]]
## [[8]]$timestep
## [1] 7
## 
## [[8]]$proxel
##    state tau tau_k    prob prev
## 1      2   3     7 0.36450    1
## 2      3   0     7 0.04050    1
## 4      3   1     7 0.04500    2
## 6      3   2     7 0.05000    3
## 8      2   4     7 0.32805    4
## 9      3   0     7 0.03645    4
## 11     3   1     7 0.04050    5
## 13     3   2     7 0.04500    6
## 15     3   3     7 0.05000    7
## 
## 
## [[9]]
## [[9]]$timestep
## [1] 8
## 
## [[9]]$proxel
##    state tau tau_k        prob prev
## 1      2   4     8 0.275978571    1
## 2      3   0     8 0.036450000    1
## 3      4   0     0 0.052071429    1
## 4      3   1     8 0.034714286    2
## 5      4   0     0 0.005785714    2
## 6      3   2     8 0.038571429    3
## 7      4   0     0 0.006428571    3
## 8      3   3     8 0.042857143    4
## 9      4   0     0 0.007142857    4
## 10     2   5     8 0.248380714    5
## 11     3   0     8 0.032805000    5
## 12     4   0     0 0.046864286    5
## 13     3   1     8 0.031242857    6
## 14     4   0     0 0.005207143    6
## 15     3   2     8 0.034714286    7
## 16     4   0     0 0.005785714    7
## 17     3   3     8 0.038571429    8
## 18     4   0     0 0.006428571    8
## 19     3   4     8 0.042857143    9
## 20     4   0     0 0.007142857    9
## 
## 
## [[10]]
## [[10]]$timestep
## [1] 9
## 
## [[10]]$proxel
##    state tau tau_k        prob prev
## 1      2   5     9 0.202384286    1
## 2      3   0     9 0.027597857    1
## 3      4   0     0 0.045996429    1
## 4      3   1     9 0.030375000    2
## 5      4   0     0 0.006075000    2
## 7      3   2     9 0.028928571    4
## 8      4   0     0 0.005785714    4
## 10     3   3     9 0.032142857    6
## 11     4   0     0 0.006428571    6
## 13     3   4     9 0.035714286    8
## 14     4   0     0 0.007142857    8
## 16     2   6     9 0.182145857   10
## 17     3   0     9 0.024838071   10
## 18     4   0     0 0.041396786   10
## 19     3   1     9 0.027337500   11
## 20     4   0     0 0.005467500   11
## 22     3   2     9 0.026035714   13
## 23     4   0     0 0.005207143   13
## 25     3   3     9 0.028928571   15
## 26     4   0     0 0.005785714   15
## 28     3   4     9 0.032142857   17
## 29     4   0     0 0.006428571   17
## 31     3   5     9 0.035714286   19
## 32     4   0     0 0.007142857   19
## 
## 
## [[11]]
## [[11]]$timestep
## [1] 10
## 
## [[11]]$proxel
##    state tau tau_k        prob prev
## 1      2   6    10 0.141669000    1
## 2      3   0    10 0.020238429    1
## 3      4   0     0 0.040476857    1
## 4      3   1    10 0.022078286    2
## 5      4   0     0 0.005519571    2
## 7      3   2    10 0.024300000    4
## 8      4   0     0 0.006075000    4
## 10     3   3    10 0.023142857    6
## 11     4   0     0 0.005785714    6
## 13     3   4    10 0.025714286    8
## 14     4   0     0 0.006428571    8
## 16     3   5    10 0.028571429   10
## 17     4   0     0 0.007142857   10
## 19     2   7    10 0.127502100   12
## 20     3   0    10 0.018214586   12
## 21     4   0     0 0.036429171   12
## 22     3   1    10 0.019870457   13
## 23     4   0     0 0.004967614   13
## 25     3   2    10 0.021870000   15
## 26     4   0     0 0.005467500   15
## 28     3   3    10 0.020828571   17
## 29     4   0     0 0.005207143   17
## 31     3   4    10 0.023142857   19
## 32     4   0     0 0.005785714   19
## 34     3   5    10 0.025714286   21
## 35     4   0     0 0.006428571   21
## 37     3   6    10 0.028571429   23
## 38     4   0     0 0.007142857   23
## 
## 
## [[12]]
## [[12]]$timestep
## [1] 11
## 
## [[12]]$proxel
##    state tau tau_k        prob prev
## 1      2   7    11 0.092084850    1
## 2      3   0    11 0.014166900    1
## 3      4   0     0 0.035417250    1
## 4      3   1    11 0.015178821    2
## 5      4   0     0 0.005059607    2
## 7      3   2    11 0.016558714    4
## 8      4   0     0 0.005519571    4
## 10     3   3    11 0.018225000    6
## 11     4   0     0 0.006075000    6
## 13     3   4    11 0.017357143    8
## 14     4   0     0 0.005785714    8
## 16     3   5    11 0.019285714   10
## 17     4   0     0 0.006428571   10
## 19     3   6    11 0.021428571   12
## 20     4   0     0 0.007142857   12
## 22     2   8    11 0.082876365   14
## 23     3   0    11 0.012750210   14
## 24     4   0     0 0.031875525   14
## 25     3   1    11 0.013660939   15
## 26     4   0     0 0.004553646   15
## 28     3   2    11 0.014902843   17
## 29     4   0     0 0.004967614   17
## 31     3   3    11 0.016402500   19
## 32     4   0     0 0.005467500   19
## 34     3   4    11 0.015621429   21
## 35     4   0     0 0.005207143   21
## 37     3   5    11 0.017357143   23
## 38     4   0     0 0.005785714   23
## 40     3   6    11 0.019285714   25
## 41     4   0     0 0.006428571   25
## 43     3   7    11 0.021428571   27
## 44     4   0     0 0.007142857   27
## 
## 
## [[13]]
## [[13]]$timestep
## [1] 12
## 
## [[13]]$proxel
##    state tau tau_k        prob prev
## 1      2   8    12 0.052181415    1
## 2      3   0    12 0.009208485    1
## 3      4   0     0 0.030694950    1
## 4      3   1    12 0.009444600    2
## 5      4   0     0 0.004722300    2
## 7      3   2    12 0.010119214    4
## 8      4   0     0 0.005059607    4
## 10     3   3    12 0.011039143    6
## 11     4   0     0 0.005519571    6
## 13     3   4    12 0.012150000    8
## 14     4   0     0 0.006075000    8
## 16     3   5    12 0.011571429   10
## 17     4   0     0 0.005785714   10
## 19     3   6    12 0.012857143   12
## 20     4   0     0 0.006428571   12
## 22     3   7    12 0.014285714   14
## 23     4   0     0 0.007142857   14
## 25     2   9    12 0.046963274   16
## 26     3   0    12 0.008287637   16
## 27     4   0     0 0.027625455   16
## 28     3   1    12 0.008500140   17
## 29     4   0     0 0.004250070   17
## 31     3   2    12 0.009107293   19
## 32     4   0     0 0.004553646   19
## 34     3   3    12 0.009935229   21
## 35     4   0     0 0.004967614   21
## 37     3   4    12 0.010935000   23
## 38     4   0     0 0.005467500   23
## 40     3   5    12 0.010414286   25
## 41     4   0     0 0.005207143   25
## 43     3   6    12 0.011571429   27
## 44     4   0     0 0.005785714   27
## 46     3   7    12 0.012857143   29
## 47     4   0     0 0.006428571   29
## 49     3   8    12 0.014285714   31
## 50     4   0     0 0.007142857   31
## 
## 
## [[14]]
## [[14]]$timestep
## [1] 13
## 
## [[14]]$proxel
##    state tau tau_k        prob prev
## 1      2   9    13 0.020872566    1
## 2      3   0    13 0.005218142    1
## 3      4   0     0 0.026090708    1
## 4      3   1    13 0.004604243    2
## 5      4   0     0 0.004604243    2
## 7      3   2    13 0.004722300    4
## 8      4   0     0 0.004722300    4
## 10     3   3    13 0.005059607    6
## 11     4   0     0 0.005059607    6
## 13     3   4    13 0.005519571    8
## 14     4   0     0 0.005519571    8
## 16     3   5    13 0.006075000   10
## 17     4   0     0 0.006075000   10
## 19     3   6    13 0.005785714   12
## 20     4   0     0 0.005785714   12
## 22     3   7    13 0.006428571   14
## 23     4   0     0 0.006428571   14
## 25     3   8    13 0.007142857   16
## 26     4   0     0 0.007142857   16
## 28     2  10    13 0.018785309   18
## 29     3   0    13 0.004696327   18
## 30     4   0     0 0.023481637   18
## 31     3   1    13 0.004143818   19
## 32     4   0     0 0.004143818   19
## 34     3   2    13 0.004250070   21
## 35     4   0     0 0.004250070   21
## 37     3   3    13 0.004553646   23
## 38     4   0     0 0.004553646   23
## 40     3   4    13 0.004967614   25
## 41     4   0     0 0.004967614   25
## 43     3   5    13 0.005467500   27
## 44     4   0     0 0.005467500   27
## 46     3   6    13 0.005207143   29
## 47     4   0     0 0.005207143   29
## 49     3   7    13 0.005785714   31
## 50     4   0     0 0.005785714   31
## 52     3   8    13 0.006428571   33
## 53     4   0     0 0.006428571   33
## 55     3   9    13 0.007142857   35
## 56     4   0     0 0.007142857   35
## 
## 
## [[15]]
## [[15]]$timestep
## [1] 14
## 
## [[15]]$proxel
##    state tau tau_k        prob prev
## 2      3   0    14 0.002087257    1
## 3      4   0     0 0.020872566    1
## 5      4   0     0 0.005218142    2
## 8      4   0     0 0.004604243    4
## 11     4   0     0 0.004722300    6
## 14     4   0     0 0.005059607    8
## 17     4   0     0 0.005519571   10
## 20     4   0     0 0.006075000   12
## 23     4   0     0 0.005785714   14
## 26     4   0     0 0.006428571   16
## 29     4   0     0 0.007142857   18
## 32     3   0    14 0.001878531   20
## 33     4   0     0 0.018785309   20
## 35     4   0     0 0.004696327   21
## 38     4   0     0 0.004143818   23
## 41     4   0     0 0.004250070   25
## 44     4   0     0 0.004553646   27
## 47     4   0     0 0.004967614   29
## 50     4   0     0 0.005467500   31
## 53     4   0     0 0.005207143   33
## 56     4   0     0 0.005785714   35
## 59     4   0     0 0.006428571   37
## 62     4   0     0 0.007142857   39
## 
## 
## [[16]]
## [[16]]$timestep
## [1] 15
## 
## [[16]]$proxel
##    state tau tau_k        prob prev
## 1      3   1    15 0.002087257    1
## 13     3   1    15 0.001878531   12

What is the probability that the patient is still sick after 8 days for different discrete time steps (e.g. 2, 1, 0.5, 0.25, 0.1)?

What is the probability of measuring fever on the 9th day for different discrete time steps (e.g. 2, 1, 0.5, 0.25, 0.1)?

## [1] "Wkt = 0.608"

## [1] "Wkt = 0.5284065"

## [1] "Wkt = 0.52882555229399"

## [1] "Wkt = 0.52913153254786"

## [1] "Wkt = 0.536988812479435"

What is the expected duration until healing with probability 99% for different discrete time steps (e.g. 2, 1, 0.5, 0.25, 0.1)?

##   state tau tau_k    prob prev
## 2     3   0    14 0.01792    1

## [1] "Für 2 An Tag: 12"

##    state tau tau_k        prob prev
## 2      3   0    14 0.002087257    1
## 32     3   0    14 0.001878531   20

## [1] "Für 1 An Tag: 14"

##     state tau tau_k         prob prev
## 2       3   0    14 0.0002843604    1
## 62      3   0    14 0.0002701424   40
## 125     3   0    14 0.0002566352   81
## 191     3   0    14 0.0002438035  124

## [1] "Für .5 An Tag: 14"

##     state tau tau_k         prob prev
## 2       3   0    14 3.761015e-05    1
## 122     3   0    14 3.666990e-05   80
## 245     3   0    14 3.575315e-05  161
## 371     3   0    14 3.485932e-05  244
## 500     3   0    14 3.398784e-05  329
## 632     3   0    14 3.313814e-05  416
## 767     3   0    14 3.230969e-05  505
## 905     3   0    14 3.150194e-05  596

## [1] "Für .25 An Tag: 14"