Markov Model of Disease Development and Recovery

Markov models are commonly used to simulate diseases and allow modeling of multiple health states and outcomes. Starting with the well known Le Bras multistate model (cascading failure model) with time-independent transitions we will see how simple Markov mortality models may be pressed into the service of survival and event history analysis. We will focus on more complex models which will be able to take into account remission, recovery or other outcomes of therapy. We will discuss explicit, analytical solutions for survival functions and mortality rates of a model that can be described as a birth-and-death process with killing with linear rates as well as parametric estimation from panel data. We illustrate our theoretical findings with analysis of real and simulated data.