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3. In a simple healthy-sick model without recovery transition, a patient spends an average ten years in healthy state before getting sick or die. While the expected remaining lifetime of a sick-patient is five years. In the absence of recovery transition, the probability that a patient moves from healthy state to sick is 60% of chance. (a) Use a continuous-time homogeneous Markov chain X = (X,,t > 0} for analysis of such model. State the required assumptions and draw the transition diagram. (b) On recalling that the probability ij of making a jump between two states i and j is Tij qij/qi, derive the intensity matrix of the Markov chain. (c) Use the Kolmogorov equation (1) to find the transition probability PHD(t) = P(X = DIX H) of an healthy patient would survive for ≥ 0 period of time. (d) Find the expected lifetime of an healthy patient.

3. In a simple healthy-sick model without recovery transition, a patient spends an average ten years in healthy state before getting sick or die. While the expected remaining lifetime of a sick-patient is five years. In the absence of recovery transition, the probability that a patient moves from healthy state to sick is 60% of chance. (a) Use a continuous-time homogeneous Markov chain X = (X,,t > 0} for analysis of such model. State the required assumptions and draw the transition diagram. (b) On recalling that the probability ij of making a jump between two states i and j is Tij qij/qi, derive the intensity matrix of the Markov chain. (c) Use the Kolmogorov equation (1) to find the transition probability PHD(t) = P(X = DIX H) of an healthy patient would survive for ≥ 0 period of time. (d) Find the expected lifetime of an healthy patient.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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3. In a simple healthy-sick model without recovery transition, a patient spends an average ten years in healthy state before getting sick or die. While the expected remaining lifetime of a sick-patient is five years. In the absence of recovery transition, the probability that a patient moves from healthy state to sick is 60% of chance. (a) Use a continuous-time homogeneous Markov chain X = (X,,t > 0} for analysis of such model. State the required assumptions and draw the transition diagram. (b) On recalling that the probability ij of making a jump between two states i and j is Tij qij/qi, derive the intensity matrix of the Markov chain. (c) Use the Kolmogorov equation (1) to find the transition probability PHD(t) = P(X = DIX H) of an healthy patient would survive for ≥ 0 period of time. (d) Find the expected lifetime of an healthy patient.
Transcribed Image Text:3. In a simple healthy-sick model without recovery transition, a patient spends an average ten years in healthy state before getting sick or die. While the expected remaining lifetime of a sick-patient is five years. In the absence of recovery transition, the probability that a patient moves from healthy state to sick is 60% of chance. (a) Use a continuous-time homogeneous Markov chain X = (X,,t > 0} for analysis of such model. State the required assumptions and draw the transition diagram. (b) On recalling that the probability ij of making a jump between two states i and j is Tij qij/qi, derive the intensity matrix of the Markov chain. (c) Use the Kolmogorov equation (1) to find the transition probability PHD(t) = P(X = DIX H) of an healthy patient would survive for ≥ 0 period of time. (d) Find the expected lifetime of an healthy patient.
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