Epstein-Barr virus (EBV) is an important human pathogen that establishes a lifelong persistent infection and for which no precise animal model exists. In this paper we describe in detail an agentbased model and computer simulation of EBV infection. Agents representing EBV and sets of B and T lymphocytes move and interact on a three-dimensional grid approximating Waldeyer's ring, together with abstract compartments for lymph and blood. The simulation allows us to explore the development and resolution of virtual infections in a manner not possible in actual human experiments. Specifically, we identify parameters capable of inducing clearance, persistent infection, or death.