I'm struggling to understand what one of the key assumptions of a Markov survival model. There are three key assumptions stated:
Take for example a simple HSD model (Where state 1 denotes healthy, state 2 denotes Sick and state 3 denotes dead), $x$ in the subscript denotes the age of the individual being observed.
1) The probability of death in a short period of time $\hat{t} \approx \phi_{x+t}^{12}*\hat{t}$ (For $\phi_{x+t}^{12}$ denoting the transition intensity between states 1 and 2)
2)Markov Property
3) For some t, where $0\leq t\leq1$, constant transition intensity is assumed. This means that $\phi_{x+t}^{12} = \phi_{x}^{12}$, for some integer age $x$.
I read that as a result of this third assumption, as you view increasing ages, the force increases each year. ( $\phi_{x}^{12} < \phi_{x+1}^{12} <...<\phi_{x+n}^{12}, n\in \mathbb{Z}^{+}) $.
My question is, does making this assumption (3) mean that for other transitions (say $\phi_x^{21}$), the same would occur? And I ask if there is an underlying issue with this because I am curious whether this means if you have a state where clearly the opposite will happen ( $\phi_{x}^{ab} > \phi_{x+1}^{ab} >...>\phi_{x+n}^{ab}$), you are making the assumption that the opposite happens in the case of this Markov Survival model...