RNA viruses, such as influenza and Severe Acute Respiratory Syndrome (SARS), invoke excessive immune responses; however, the kinetics that regulate inflammatory responses within infected cells remain unresolved. Here, we develop a mathematical model of the RNA virus sensing pathways, to determine the intracellular events that primarily regulate interferon, an important protein for the activation and management of inflammation. Within the ordinary differential equation (ODE) model, we incorporate viral replication, cell death, interferon stimulated genes’ antagonistic effects on viral replication, and virus sensor protein (TLR and RIG-I) kinetics. The model is parameterized to influenza infection data using Markov chain Monte Carlo and then validated against infection data from an NS1 knockout strain of influenza, demonstrating that RIG-I antagonism significantly alters cytokine signaling trajectory. Global sensitivity analysis suggests that paracrine signaling is responsible for the majority of cytokine production, suggesting that rapid cytokine production may be best managed by influencing extracellular cytokine levels. As most of the model kinetics are host cell specific and not virus specific, the model presented provides an important step to modeling the intracellular immune dynamics of many RNA viruses, including the viruses responsible for SARS, Middle East Respiratory Syndrome (MERS), and Coronavirus Disease (COVID-19).