Use a three-state <continuous-time multi-state model> with transient infected state $I$ and absorbing recovered and dead states $R$ and $D$. If recovery and death have constant <transition intensities> $\gamma$ and $\mu$, its <Q-matrix> is
$$
Q=
\begin{pmatrix}
-(\gamma+\mu)&\gamma&\mu\\
0&0&0\\
0&0&0
\end{pmatrix},
$$
with state order $(I,R,D)$. This is also a <competing risks model>: recovery and death are the two mutually exclusive first events.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 1 / d / Solution

{title2=$q_{rs}(t)$}

The transition intensity $q_{rs}(t)$ is the instantaneous rate of moving from state $r$ to state $s$, conditional on occupying state $r$ immediately before time $t$.


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 Incoming links: Transition intensity