Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 207 / 2 / a / Solution

Use a two-state continuous-time Markov chain with uninfected state $S$ and infected state $I$:The generator is $Q=\left(\begin{array}{cc}-a& a\\ b& -b\end{array}\right)$. Exponential holding times give expected time from recovery to the next infection $1/a$ and expected infection duration $1/b$.