The presence of cells latently infected with HIV is currently considered to be a major barrier to viral eradication within a patient. Here, we consider birth–death-immigration models for the latent cell population in a single patient, and present analytical results for the size of this population in the absence of treatment. We provide results both at steady state (viral set point), and during the non-equilibrium setting of early infection. We obtain semi-analytic results showing how latency-reversing drugs might be expected to affect the size of the latent pool over time. We also analyze the probability of rare mutant viral strains joining the latent cell population, allowing for steady-state and dynamic viral populations within the host.