Modeling lung cancer using systems of differential equations

Abstract

Mathematical modeling provides a rigorous formal framework for describing the biological processes involved in the onset and progression of lung cancer. Systems of differential equations-exceptionally powerful analytical tools-enable the quantitative description of tumor growth, the interactions between tumor cells and immune system components, and the impact of various therapeutic interventions such as chemotherapy, radiotherapy, surgery, and immunotherapy. Unlike clinical observation, which captures the disease at discrete time points, mathematical models describe the continuous temporal evolution of cell populations and allow for the simulation of therapeutic scenarios without risk to the patient. The numerical results obtained align well with clinical observations and the specialized literature, serving as a form of qualitative validation for the implemented models. In the following section, we discuss the key aspects confirming the biological plausibility of the simulations, as well as the limitations that should be considered during interpretation. First, the behavior of the tumor-immune system model in the absence of treatment-tending toward a state of coexistence-corresponds to the clinical phenomenon of "immunologic equilibrium," wherein the tumor is kept at a reduced size by the immune system without being eliminated. This behavior reproduces one of the three phases of the cancer theory (elimination, equilibrium, and escape), thereby confirming the model's biological relevance.