Mean Time in Illness Death Model











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I would like to calculate the mean time "alive" for a progressive, time homogenous, three state Markov model in continous time. It is an illness-death model with three states: healthy, ill, dead. Illness cannot be reversed. Death is absorbing.



The initial numbers of patients in the three states are $S_0={N_h,N_i,0}$. The transition rate matrix is
$Q=begin{bmatrix}
-a-b & a & b\
0 &-c & c\
0 & 0 & 0
end{bmatrix}$
.



The transition probability matrix is calculated using the matrix exponential, $P(t) = e^{Qt}$.



Is there a way to calculate the mean time in the "alive" state, that is healthy or alive?










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    down vote

    favorite












    I would like to calculate the mean time "alive" for a progressive, time homogenous, three state Markov model in continous time. It is an illness-death model with three states: healthy, ill, dead. Illness cannot be reversed. Death is absorbing.



    The initial numbers of patients in the three states are $S_0={N_h,N_i,0}$. The transition rate matrix is
    $Q=begin{bmatrix}
    -a-b & a & b\
    0 &-c & c\
    0 & 0 & 0
    end{bmatrix}$
    .



    The transition probability matrix is calculated using the matrix exponential, $P(t) = e^{Qt}$.



    Is there a way to calculate the mean time in the "alive" state, that is healthy or alive?










    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I would like to calculate the mean time "alive" for a progressive, time homogenous, three state Markov model in continous time. It is an illness-death model with three states: healthy, ill, dead. Illness cannot be reversed. Death is absorbing.



      The initial numbers of patients in the three states are $S_0={N_h,N_i,0}$. The transition rate matrix is
      $Q=begin{bmatrix}
      -a-b & a & b\
      0 &-c & c\
      0 & 0 & 0
      end{bmatrix}$
      .



      The transition probability matrix is calculated using the matrix exponential, $P(t) = e^{Qt}$.



      Is there a way to calculate the mean time in the "alive" state, that is healthy or alive?










      share|cite|improve this question













      I would like to calculate the mean time "alive" for a progressive, time homogenous, three state Markov model in continous time. It is an illness-death model with three states: healthy, ill, dead. Illness cannot be reversed. Death is absorbing.



      The initial numbers of patients in the three states are $S_0={N_h,N_i,0}$. The transition rate matrix is
      $Q=begin{bmatrix}
      -a-b & a & b\
      0 &-c & c\
      0 & 0 & 0
      end{bmatrix}$
      .



      The transition probability matrix is calculated using the matrix exponential, $P(t) = e^{Qt}$.



      Is there a way to calculate the mean time in the "alive" state, that is healthy or alive?







      markov-chains markov-process






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      asked Nov 23 at 17:28









      MPahuta

      1598




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