The role of the host immune response in determining the severity and duration of an influenza infection is still unclear. In order to identify severity factors and more accurately predict the course of an influenza infection within a human host, an understanding of the impact of host factors on the infection process is required. Despite the lack of sufficiently diverse experimental data describing the time course of the various immune response components, published mathematical models were constructed from limited human or animal data using various strategies and simplifying assumptions. To assess the validity of these models, we assemble previously published experimental data of the dynamics and role of cytotoxic T lymphocytes, antibodies, and interferon and determined qualitative key features of their effect that should be captured by mathematical models. We test these existing models by confronting them with experimental data and find that no single model agrees completely with the variety of influenza viral kinetics responses observed experimentally when various immune response components are suppressed. Our analysis highlights the strong and weak points of each mathematical model and highlights areas where additional experimental data could elucidate specific mechanisms, constrain model design, and complete our understanding of the immune response to influenza.