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The transition probability matrix has entriesunder the time-homogeneous Markov property. For the finite-state model in part d, the transition semigroup of a continuous-time Markov chain is

The model assumes a time-homogeneous Markov property: transition intensities depend only on the current state, not on calendar time, infection age, or earlier history. A Semi-Markov multi-state model could let recovery and death hazards depend on time since infection or entry into the current state. Weekly tests reveal recovery only by interval censoring, however, so the relevant entry and transition times are latent. Fitting the less restrictive model then requires integrating over unobserved paths, and the available data may contain too little information to identify a flexible duration-dependent hazard.