Three-state irreversible disease model
= Three-state irreversible disease model
{title2=$Q=\begin{pmatrix}-\lambda&\lambda&0\\0&-\nu&\nu\\0&0&0\end{pmatrix}$}
A sequential <continuous-time Markov chain> has transitions $1\to2\to3$ with rates $\lambda,\nu$ and an <absorbing state> $3$. Its probability of ever leaving state $1$ by time $t$ is $1-e^{-\lambda t}$; its probability of occupying state $2$ is $\lambda(e^{-\lambda t}-e^{-\nu t})/(\nu-\lambda)$ for unequal rates.