Kinetic model of HIV infection including hematopoietic progenitor cells

Markov process models of the dynamics of HIV reservoirs

While latently infected CD4+ T cells are extremely sparse, they are a reality that prevents HIV from being cured, and their dynamics are largely unknown. We begin with a two-state Markov process that models the outcomes of regular but infrequent blood tests for latently infected cells in an HIV positive patient under drug therapy. We then model the hidden dynamics of a latently infected CD4+ T cell in an HIV positive patient and show there is a limiting distribution, which indicates in which compartments the HIV typically can be found. Our model shows that the limiting distribution of latently infected cells reveals the presence of latency in every compartment with positive probability, supported by clinical data. We also show that the hidden Markov model determines the outcome of blood tests and analyze its connection to the blood test model.

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.