Nonlinear dynamics of cell migration between two cancer centers

Abstract

A theoretical model explaining the evolution of two cancer centers through the concentration of T-lymphocytes is presented. The model explores how variations in T-lymphocyte parameters and cellular diffusion rates affect the system’s dynamics. It also investigates the conditions under which the system transitions from continuous wave evolution to periodic oscillations and chaotic regimes. Depending on certain parameter values, the system can exhibit a variety of dynamic behaviors: continue waves that manifest a stable equilibrium of the system; periodic and quasi-periodic oscillations, and finally chaotic regimes in which the system becomes unpredictable. The considered model indicates that cell migration between tumors may have a significant impact on disease progression and immune response, e.g., chaotic behavior may reflect increased variability in disease progression, which could complicate therapeutic strategies. Understanding of this dynamic behavior of cells may contribute to the development of more effective approaches to cancer treatment, taking into account the complex interactions between multiple tumor locals and the immune system. These findings shed light on the intricate behavior of immune-tumor interactions and could lead to more effective cancer treatment strategies. In conclusion, the cancer progression can be predicted by the mathematical modeling of metastasis and good therapeutically strategies and targeting cell migration can be achieved.