  The recent advances in cancer immunotherapy paved the way for the development
of tumor-immune system mathematical models aiming to provide the missing
mechanistic understanding and indicate more efficient treatment regimes.
However, the complexity of such models, their multi-scale dynamics and their
overparameterized character renders them inaccessible for wide utilization and
hinders the acquisition of physical understating. Here, a fundamental and
overparameterized model formulating the interactions of tumor cells with
natural killer cells, CD8+ T cells and circulating lymphocytes is adopted. It
is first shown that the long-term evolution of the system towards the
high-tumor or the tumor-free equilibrium is determined by the dynamics of an
initial explosive stage of tumor progression. Focusing on this stage, the
algorithmic Computational Singular Perturbation methodology is employed to
identify the underlying mechanisms confining the system to evolve towards the
high-tumor equilibrium and the governing slow dynamics along them. It is
further demonstrated that this approach can successfully predict the response
of the system in parameter perturbations. This preliminary analysis
demonstrates the potential of algorithmic asymptotic analysis to simplify the
complex, overeparameterized and multi-scale cancer immunology models and to
indicate the interactions and cell types to target for more effective treatment
development.
