Markov process models of the dynamics of HIV reservoirs

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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.