Discrete-time multi-state diagnosis model
= Discrete-time multi-state diagnosis model
{title2=$e_k=ah_{k-1}$}
With a one-step early state, early diagnosis probability $a$, and non-early diagnosis probability $b$ per subsequent step, mean infections $h_i$ yield early diagnoses $e_k=ah_{k-1}$ and late diagnoses $n_k=b(1-a)\sum_{i\leq k-2}h_i(1-b)^{k-i-2}$. The early intensity fraction is $e_k/(e_k+n_k)$ when positive. Initial infections and endpoint conventions determine the index limits.