ДИСКРЕТНІ МОДЕЛІ КЛІТИННИХ АВТОМАТІВ ДИНАМІКИ РОСТУ ПУХЛИНИ ТА ІМУННОГО НАГЛЯДУ

Mathematical modeling and simulation play a central role in elucidating tumor growth dynamics and evaluating therapeutic interventions in oncology. A cellular automata approach consisting of three discrete models of increasing complexity was investigated: (i) an uncontrolled proliferation model capturing exponential tumor expansion; (ii) a spatially constrained proliferation model reproducing logistic-like saturation due to microenvironmental limits; and (iii) an immune response model incorporating effector cell interactions and cytokine-mediated chemotaxis. These models operate on two-dimensional lattices with stochastic update rules calibrated by biologically relevant division and death rates. Simulation experiments demonstrate that the uncontrolled model reproduces classical exponential growth behavior, while the spatially constrained model yields sigmoidal growth curves consistent with Verhulst dynamics. The immune response model further enables simulation of interactions among tumor cells, effector lymphocytes, and cytokine signals, capturing complex biological dynamics that are difficult to derive or compute with traditional analytical methods. Parameter sensitivity analyses reveal critical regimes of cytokine secretion and effector recruitment that govern the transition between tumor containment and escape. This discrete, rule-based model provides a powerful tool for exploring tumor-immune interactions and evaluating potential treatment strategies.