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

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