When modeling spread of disease, heterogeneities in contact structure and stochastic modes of transmission are essential to accurately predict the size of an outbreak. Agent-based models are commonly used to capture this level of granularity, however, simulating them can be computationally expensive. Probability generating functions (PGFs) offer an efficient framework for describing stochastic transmission on a contact network. In this talk, I will introduce the PGF framework for network contagion processes and illustrate its usefulness through two examples. First, I will demonstrate how this framework can be extended with a time-dependent PGF and flexible transmission expression to investigate the timing and strength of interventions on epidemic spread. These findings can apply intervention strategies such as vaccination, masking, social distancing, and treatments to the spreading process. Second, I will demonstrate the sensitivity of this framework and how error effects final outbreak size results. Lastly, I will discuss my plans to apply this type of analysis to other epidemiological PGF applications.