This study explores the natural control system in the body for responding to exposure to the Influenza A virus. More specifically, it delves into the development of a model to simulate the responses of target uninfected cell counts, infected cell counts, and viral titers. There are two particular models of interest: a delayed model that incorporates the brief inactive period for newly infected cells, and a non-delayed model reflecting only infected cells without delay after initial infection. Both models are commonly used in the literature and the benefits of each model are studied and explained. We generate Simulink models for both the delayed and non-delayed sets of ordinary differential equations (ODEs) to simulate responses to different viral titer impulses. Additionally, this study aims to extrapolate these models to the case for a vaccinated individual. To do this, we modify the viral clearance rate and infected cell death rate of our initial model to account for the improved immune response generated by vaccines.