Consider a continuous-time Markov process with 4 consecutive states (1: mild, 2: moderate, 3: severe, 4: critical) and an absorbing state death (5) where patients can move from state i to j among adjacent states. Also, consider that the patient can die from any state (1, 2, 3, 4). i.e. there is a possibility of immediately transitioning from state 1, 2, 3, 4 to state 5.
a) Define Transition Intensity as opposed to transition probability.
b) What is a Q matrix and how is it generated? What are the characteristics of the Q matrix (details)?
c) Provide a mathematically calculated example of the described system and show how you calculated both the intensities and probabilities. Please don't use any programming software. Provide mathematical answers with detailed explanations.