Solution
= Solution
For a treated patient the recovery <transition intensity> is $\mu_T=0.25\times2=0.5$ per year. A symptoms spell is a <holding time> with an <exponential distribution> of rate $\mu_T$, so
$$
\boxed{\mathbb E(\text{length of a treated symptoms spell})=\frac1{0.5}=2\text{ years}.}
$$
The treatment multiplier for onset affects how often symptoms begin, not the duration of a spell once the patient is in state 2, under this homogeneous <continuous-time Markov chain>.