Ordinary Differential Equations (ODEs) and Agent-Based Models (ABMs) represent nowadays the two main approaches for Immune System (IS) modeling. While the former approach does not allow for representing aleatory variations, the latter lacks a clear well-defined semantics, entailing possible biases on simulation results. We present here the application of our modeling pipeline, that has been designed to cope with these shortcomings, to a case-study about the competition between cancer and IS under the administration of a pre-clinical vaccine in transgenic mice. The pipeline involves the use of Extended Stochastic Symmetric Nets (ESSN) for a formal definition of the conceptual model, and allows to study the domain problem from a macro-perspective by means of the Stochastic Simulation Algorithm (SSA) or from a micro-perspective through an Agent Based Model with a clear defined semantics. The numerical results obtained in this study using SSA are presented and global sensitivity analysis is performed using Latin Hypercube Sampling - Partial Rank Correlation Coefficients (LHS-PRCC) to analyze and improve vaccine dosages and timings.