A Mathematical Model on the Immune System Role in Achieving Better Outcomes of Cancer Chemotherapy

The incidence of neoplastic diseases shows that the search for more effective cancer treatments is still necessary. In addition to standard treatments such as chemo- and radiotherapy, new treatment modalities have been focused in recent advances in immunology. Since little has been discussed about the biological implications of chemotherapy with respect to its impact on the immune system and on the other normal, ``healthy'' cells, we devote the present mathematical modeling work to do so. First, we prove the invariance of the region where all state variables remain positive (i.e., the number of cancer cells, normal cells and immune cells, and the amount of chemotherapy); afterwards, we analyze the model in terms of the linear stability of the system, and we establish a necessary and sufficient condition for the local stability of the {\it{cure}} equilibrium point. Moreover, we simulate some scenarios involving both the immune system and chemotherapy, showing that a reasonable treatment strategy occurs when these are combined suitably.