Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 207 / 3 / c / ii / Solution

The untreated rates are ${\lambda }_U=0.2$ and ${\mu }_U=0.25$; treatment changes them to ${\lambda }_T=0.2\times 0.8=0.16$ and ${\mu }_T=0.25\times 2=0.5$. Their stationary distributions give symptoms fractionsConsequentlyThus 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.