Exploring tumor-induced immunosuppression dynamics by myeloid-derived suppressor cells: insights via a fractional-order mathematical model

This study investigates the intricate role of myeloid-derived suppressor cells (MDSCs) in inhibiting the immunological responses against malignancies by employing a delayed fractional-order mathematical model. The proposed mathematical model includes tumor cells, dendritic cells, macrophages, cytotoxic T lymphocytes (CTLs), and MDSCs as components of a five-dimensional deterministic system. Further, the model accounts for the duration of the mechanism by which MDSCs perform immunosuppressive activities. One such mechanism involves the release of immunosuppressive cytokines such as interleukin-10 (IL-10), and it is elucidated by incorporation of the time-delay parameter, \(\tau\). Basic properties of the system such as non-negativity and uniqueness of solutions as well as the existence of biologically feasible steady states are explored. The conditions for steady-state stability and existence of Hopf bifurcation concerning the delay parameter \((\tau )\) are established. We notice that the growth rate of cancer cells determines the stability nature of the tumor-free equilibrium, regardless of the time-delay \(\tau\). While the fractional-order \(\alpha\) does not affect the stability of steady states, however it does influence the transient behavior of the considered system.