Dynamic behavior analysis of a fractal tumor-immune model with drug resistance

Chemotherapy is a type of treatment that uses drugs to treat cancer and prevent tumor growth. Different chemotherapy protocols and procedures have been developed. Mathematical models have been proposed to analyze the dynamical processes related to cancerous cell proliferation. In this work, we propose a fractal model with healthy, cancerous cells, and chemotherapeutic agents, as well as effector immune cells interacting with cancerous cells. The model incorporates cancer drug resistance as a result of mutation processes triggered by chemotherapy. We demonstrate that the order of our fractal tumor-immune model influences the time evolution of cell population. Considering three different cancer therapy protocols, we observe that the maximum cancerous cells and the time interval for that maximal to be reached depend significantly on the initial conditions of the number of host and cancer cells. Our results show that the protocols play a crucial role in cancer treatment, and the protocol can result in a better result of cancerous cell suppression.