Delay model of tumor-immune system interactions with hyperthermia treatment

Abstract

The interaction of the tumor-immune system was initially based on the immunosurveillance hypothesis that immune cells can identify and kill tumor cells, leading to the use of a prey-predatory model for the description of tumor-immune cell interactions. However, the current biomedical findings reveal a pathway to immunoediting, which hypothesizes the ability of tumors to inhibit, seal, and counteract effector cells. Contrary to the discovery of non-oscillating dynamic biomedicine in solid tumors, existing models show oscillating solutions. Thus, the formulation of an immunoediting model that corresponds to the interaction of the tumor-immune system is sacrosanct in the search for effective malignant tumor treatment. The research suggests an immunoediting delay model of tumor-immune system interactions that combine tumor-immune cytokines derived from tumors to counteract effector cells. Qualitative analysis of this model gives an idea of the conditions for the stability of non-aggressive (benign) tumors and the instability of aggressive (malignant) tumors. The numerical results for these two conditions do not indicate an oscillating solution. Although the elimination of tumors is seen in the case of non-aggressive tumors, the suppression of effector cells and uncontrolled growth of tumors characterize the results for aggressive tumors. To find the best treatment, a sensitivity analysis is performed to ensure the role of the model parameters in the development of the tumor. The analysis reveals the best treatment options to kill tumor cells and strengthen the performance of immune cells. The sensitivity analysis results inform the merger of hyperthermia treatments in the proposed model to investigate the effects of thermal induction on immune cell performance and tumor regression. Discrete-time delays were used to investigate whether hyperthermia treatment was safe for patients who had received other treatments, but no cure occurred. The global stability of hyperthermia treatment is obtained using the Lyapunov function. Furthermore, an optimal heat control strategy for treating malignant tumor hyperthermia is obtained to minimize the effect of heat on normal cells while ensuring the elimination of malignant tumors. This research establishes a unique thermal optimal solution that improves the performance of the effector cell without difficulty.