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The question of when to initiate HIV treatment is considered the most important question in HIV care today. Benefits of delaying therapy include avoiding the negative side effects and toxicities associated with the drugs, delaying selective pressures that induce the development of resistant strains of the virus, and preserving a limited number of treatment options. On the other hand, the risks of delayed therapy include the possibility of irreversible damage to the immune system, development of AIDS-related complications, and death. We use Markov decision processes to develop the first HIV optimization models that aim to maximize the expected lifetime or quality-adjusted lifetime of a patient. We prove conditions that establish structural properties of the optimal solution and compare them to our data and results. Model solutions, based on clinical data, support a strategy of treating HIV earlier in its course as opposed to …