| Description |
Mathematical models of tumor-immune interactions provide an analytical framework by which to address specific questions about tumor-immune dynamics. We present an extension of a mathematical model developed by De Pillis et al. that accounts for the immune surveillance of tumors by natural killer (NK) cells and cytotoxic CD8+ T lymphocytes (CTL's). NK cells mediate an innate immune response against cancer because NK cells can respond to tumor cells without the need for prior antigen-specific stimulation, while CTL's mediate an adaptive immune response because they require antigen-specific stimulation before responding effectively. Our extended model incorporates state transitions between naive and primed CTL's and cytokine signaling between NK cells and CTL's. In addition, the model describes tumor-immune interactions focusing on the roles of the innate and adaptive immune responses in tumor immune surveillance. The mathematical model describes tumor-immune interactions by utilizing a system of non-linear differential equations with respect to tumor cells, NK cells, CTL's, and antigen presenting cells. The functions describing tumor-immune growth, antigen presentation, immune response, and interaction rates are numerically simulated with a differential equation solver (GNU Octave). Parameter estimates and model validations are obtained from prior mathematical papers and medical studies related to this topic. We expect that both the innate and adaptive immune systems play independent and synergistic roles to defend the body from cancer. |
