Markov cellular automata models for chronic disease progression

We analyze a Markov cellular automaton that models the spread of viruses that often progress to a chronic condition, such as human immunodeficiency virus (HIV) or hepatitis C virus (HCV). We show that the complex dynamical system produces a Markov process at the later stages, whose eigenvectors corresponding to the eigenvalue 1 have physical significance for the long-term prognosis of the virus. Moreover we show that drug treatment leads to chronic conditions that can be modeled by Markov shifts with more optimal eigenvectors.