Tuberculosis (TB) is the leading cause of death by an infectious agent, and developing an effective vaccine is an important component of the WHO's EndTB Strategy. Non-human primate (NHP) models of vaccination are crucial to TB vaccine development and have informed design of subsequent human trials. However, challenges emerge when translating results from animal models to human applications, and connecting post-vaccination immunological measurements to infection outcomes. The H56:IC31 vaccine is a candidate currently in phase I/IIa trials. H56 is a subunit vaccine that is comprised of 3 mycobacterial antigens: ESAT6, Ag85B, and Rv2660, formulated in IC31 adjuvant. H56, as a boost to Bacillus Calmette-Guérin (BCG, the TB vaccine that is currently used in most countries world-wide) demonstrates improved protection (compared to BCG alone) in mouse and NHP models of TB, and the first human study of H56 reported strong antigen-specific T cell responses to the vaccine. We integrated NHP and human data with mathematical modeling approaches to improve our understanding of NHP and human response to vaccine. We use a mathematical model to describe T-cell priming, proliferation, and differentiation in lymph nodes and blood, and calibrate the model to NHP and human blood data. Using the model, we demonstrate the impact of BCG timing on H56 vaccination response and reveal a general immunogenic response to H56 following BCG prime. Further, we use uncertainty and sensitivity analyses to isolate mechanisms driving differences in vaccination response observed between NHP and human datasets. This study highlights the power of a systems biology approach: integration of multiple modalities to better understand a complex biological system.