The cellular immune response to primary influenza virus infection is complex, involving multiple cell types and anatomical compartments, and is difficult to measure directly. Here we develop a two-compartment model that quantifies the interplay between viral replication and adaptive immunity. The fidelity of the model is demonstrated by accurately confirming the role of CD4 help for antibody persistence and the consequences of immune depletion experiments. The model predicts that drugs to limit viral infection and/or production must be administered within 2 days of infection, with a benefit of combination therapy when administered early, and cytotoxic CD8 T cells in the lung are as effective for viral clearance as neutralizing antibodies when present at the time of challenge. The model can be used to investigate explicit biological scenarios and generate experimentally testable hypotheses. For example, when the adaptive response depends on cellular immune cell priming, regulation of antigen presentation has greater influence on the kinetics of viral clearance than the efficiency of virus neutralization or cellular cytotoxicity. These findings suggest that the modulation of antigen presentation or the number of lung resident cytotoxic cells and the combination drug intervention are strategies to combat highly virulent influenza viruses. We further compared alternative model structures, for example, B-cell activation directly by the virus versus that through professional antigen-presenting cells or dendritic cell licensing of CD8 T cells.