= Solution
The untreated rates are $\lambda_U=0.2$ and $\mu_U=0.25$; treatment changes them to $\lambda_T=0.2\times0.8=0.16$ and $\mu_T=0.25\times2=0.5$. Their <stationary distributions> give symptoms fractions
$$
\pi_{2,U}=\frac{0.2}{0.45}=\frac49,\qquad \pi_{2,T}=\frac{0.16}{0.66}=\frac8{33}.
$$
Consequently
$$
\boxed{\frac{\pi_{2,T}}{\pi_{2,U}}=\frac{8/33}{4/9}=\frac6{11}.}
$$
Thus the estimated long-run symptoms fraction under treatment is about 54.5% of the untreated fraction. This combines less frequent onset with faster recovery; it is not either individual <hazard ratio> alone.
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