Investigating the Relationship Between Tumor Cells, Healthy Tissue, and an Active Immune System in a Mathematical Model of Cancer Cell Growth

Analyzing tumor growth dynamics improves treatment strategies for cancer. Many models have been proposed to analyze cancer development dynamics, which do not always exhibit chaotic behavior. This research aims to create and examine a unique dynamical cancer model that exhibits chaotic behavior for certain parameters. Introducing chaos into the model allows for the exploration of irregular tumor growth patterns and the identification of critical thresholds that can influence treatment outcomes. The model is examined, and each system parameter’s impact on the model’s dynamics is evaluated. The analysis of the bifurcation and Lyapunov diagrams demonstrates chaos in three populations of tumor, healthy, and immune system cells. By suppressing the immunological response, the cancer cell gains control of the chaotic attractor and establishes a stable state. This might lower the cancer condition by altering the appropriate parameter range assisting in tumor treatment.