AbstractSome viruses exhibit "rebound" when the administration of antiviral drugs is discontinued. Viral rebound caused by resistance mutations or latent reservoirs has been studied mathematically. In this study, we investigated the viral rebound due to other causes. Since immunity is weaker during antiviral treatment than without the treatment, drug discontinuation may increase the viral load. We analyzed the dynamics of the number of virus-infected cells, cytotoxic T lymphocytes, and memory cells and identified the conditions under which the viral load increased upon drug discontinuation. If drug is administered for a long time, a viral rebound occurs when the ratio of viral growth rate in the absence to that in the presence of the antiviral drug exceeds the "rebound threshold." We analyzed how the rebound threshold depended on patient's conditions and type of treatment. Mathematical and numerical analyses revealed that rebound after discontinuation was more likely to occur when the drug was effective in reducing viral proliferation, drug discontinuation was delayed, and the processes activating immune responses directly were stronger than those that occurred indirectly via immune memory formation. We discussed additional reasons for drugs to cause viral rebound more likely.