We present a simplified dynamical model of immune response to uncomplicated influenza A virus (IAV) infection, which focuses on the control of the infection by the innate and adaptive immunity. Innate immunity is represented by interferon-induced resistance to infection of respiratory epithelial cells and by removal of infected cells by effector cells (cytotoxic T-cells and natural killer cells). Adaptive immunity is represented by virus-specific antibodies. Similar in spirit to the recent model of Bocharov and Romanyukha [1994. Mathematical model of antiviral immune response. III. Influenza A virus infection. J. Theor. Biol. 167, 323-360], the model is constructed as a system of 10 ordinary differential equations with 27 parameters characterizing the rates of various processes contributing to the course of disease. The parameters are derived from published experimental data or estimated so as to reproduce available data about the time course of IAV infection in a naïve host. We explore the effect of initial viral load on the severity and duration of the disease, construct a phase diagram that sheds insight into the dynamics of the disease, and perform sensitivity analysis on the model parameters to explore which ones influence the most the onset, duration and severity of infection. To account for the variability and speed of adaptation of the adaptive response to a particular virus strain, we introduce a variable that quantifies the antigenic compatibility between the virus and the antibodies currently produced by the organism. We find that for small initial viral load the disease progresses through an asymptomatic course, for intermediate value it takes a typical course with constant duration and severity of infection but variable onset, and for large initial viral load the disease becomes severe. This behavior is robust to a wide range of parameter values. The absence of antibody response leads to recurrence of disease and appearance of a chronic state with nontrivial constant viral load.