 Illness-death model

An irreversible three-state illness-death model allows progression $1\to 2$ and death $1\to 3$ or $2\to 3$, with state 3 absorbing. A constant-rate transition intensity matrix uses three free rates $a,b,c$ and rows $(-(a+b),a,b)$, $(0,-c,c)$ and $(0,0,0)$. The labels can represent disease severity rather than literal health versus illness.