= Solution
Use three states of a <continuous-time Markov chain>: disease-free $1$, pre-clinical $2$, and clinical $3$. The <transition intensities> are $\lambda=q_{12}>0$ for onset and $\nu=q_{23}>0$ for progression. Clinical disease is an <absorbing state>. The mandatory pre-clinical phase excludes a direct $1\to3$ jump, and this untreated progression model has no reverse transitions.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/iii/paper-207-cancer-states.png]
{title=Irreversible cancer progression from disease-free to pre-clinical to clinical states}
With row-vector probabilities and state order $(1,2,3)$, \b[the generator matrix] is
$$
\boxed{Q=\begin{pmatrix}-\lambda&\lambda&0\\0&-\nu&\nu\\0&0&0\end{pmatrix}.}
$$
Its rows sum to zero, so only the two off-diagonal <transition intensities> are unknown. This is a <continuous-time multi-state model> with sequential irreversible progression.
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