= Solution
The <mean holding time from a transition intensity matrix> is $-1/q_{rr}$. Apply this to the fitted exit rates and use monotonic inversion for each <confidence interval>:
$$
\begin{aligned}
\text{mild: }&\frac1{0.0115}=86.96\text{ months},&\quad95\%\text{ CI }&=\left[\frac1{0.0130},\frac1{0.0102}\right]=[76.92,98.04],\\
\text{severe: }&\frac1{0.0318}=31.45\text{ months},&95\%\text{ CI }&=\left[\frac1{0.0352},\frac1{0.0287}\right]=[28.41,34.84].
\end{aligned}
$$
Thus the expected state durations are \b[86.96 months] and \b[31.45 months], respectively. A <confidence interval for a reciprocal rate> reverses the endpoint order; the negative diagonal rates must first be converted to positive exit rates.
For the <expected absorption time in an illness-death model>, the time spent initially in the mild state is followed by an additional severe-state duration only if progression occurs before death. That <probability> is $0.0072/0.0115$. Therefore
$$
\boxed{E_1(T_{\mathrm{death}})=\frac1{0.0115}+\frac{0.0072}{0.0115}\frac1{0.0318}=106.64\text{ months}\approx8.89\text{ years}.}
$$
This is an unconditional mean including both possible paths to death, not a mean conditional on progression.
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