= Solution
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.
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