The activation of 2'-5'-oligoadenylate synthetase (OAS) enzymes by direct interaction with viral double-stranded RNA (dsRNA) is a key part of the innate immune response to viral infection. The downstream effect of the OAS-dsRNA interaction is to degrade the viral single-stranded RNA (ssRNA) to prevent the spread of the virus. The entire OAS activation mechanism is complex and not yet well understood. Based on experimental data, the process appears to depend on concentrations and lengths of dsRNA; however, it cannot be completely observed in experiments. Hence, mathematical models can help to understand the detailed OAS activation mechanism and the effects of dsRNA lengths. Plausible biochemical scenarios are translated to mathematical models and their responses are compared to in vitro experimental data provided by McKenna's lab to test different hypotheses. In total, nine models are derived from enzyme kinetics; and their mathematical analyses and numerical investigations are provided. Model selection methods are used to determine the best model accommodating different dsRNA concentrations and lengths.