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Basic virus dynamics models have been essential in understanding quantitative issues of HIV replication. However, several parts of the viral life cycle remain elusive. One of the most critical steps is the start of viral transcription, which is governed by the regulatory protein trans‐activator of transcription (Tat) that induces a positive feedback loop. It has been shown that this feedback loop can alternate between two states leading to a transient activation of viral transcription. Using Monte Carlo simulations, we integrate the transactivation circuit into a new virus dynamics model having an age‐dependent transactivation rate and reversion into latency. The cycling of infected cells between an activated and latent state results in the typical decelerating decay of virus load following therapy. Further, we hypothesize that the activation of latently infected cells is governed by the basal transcription rate of the integrated provirus rather than the intra‐ or extracellular environment. Finally, our systems approach to modeling virus dynamics offers a promising framework to infer the extracellular dynamics of cell populations from their intracellular reaction networks.