The review presents the existing biological and mathematical models of the infection process caused by the Epstein–Barr virus. The existence of the Epstein–Barr virus in the host organism can be described by a model representing a cycle of six consecutive stages, each of them has its own independent variant of immune regulation. The phenomenon of virus excretion in biological fluids, in particular, in saliva, is modeled using differential equations. Usage of mathematical modeling allows us to supplement existing knowledge about the pathogenesis of the infectious process caused by the Epstein–Barr virus, as well as to determine threshold levels of virus isolation in non-sterile environments for the diagnosis of active forms of infection.