Parameter estimation and sensitivity analysis for a model of tumor–immune interaction in the presence of immunotherapy and chemotherapy

Abstract

Abstract A mathematical model has been utilized to examine the interaction between tumor cells and immune cells. In this model, the immune cells include natural killer cells, circulating lymphocytes, CD8+T cells, CD4+T cells, and cytokines. The model not only represents the traditional role of CD4+T cells in activating CD8+T cells but also illustrates its role in killing the tumor via the secretion of cytokines. Besides, treatments with both chemotherapy and immunotherapy are considered. However, since this model was not fitted to experimental data before, parameter estimation is performed to fit the model with experimental data, first. The estimation is validated to verify the correctness of the model using the experimental data for the tumor growth. Second, numerical experiments are performed using a set of human data. Results show the mutual relations between tumor cells, and body immune cells in the absence and in the presence of therapy. Results also show that CD4+T cells could play a crucial role in immunotherapy. Third, sensitivity analysis is performed by calculating the normalized sensitivity coefficients to identify the relative influence of body parameters on the tumor cell population. The obtained results provide a tool to identify which parameters should be increased or decreased before treatment to get the optimal immune response.

Keywords

• Mathematical modeling
• Parameter estimation
• Sensitivity analysis
• Tumor–immune interactions
• Immunotherapy
• Chemotherapy