A mathematical model for M-phase specific chemotherapy including the G0-phase and immunoresponse.
In this paper we use a mathematical model to study the effect of an M-phase specific drug on the development of cancer, including the resting phase G(0) and the immune response. The cell cycle of cancer cells is split into the mitotic phase (M-phase), the quiescent phase (G(0)-phase) and the inter phase (G(1); S; G(2) phases). We include a time delay for the passage through the interphase, and we assume that the immune cells interact with all cancer cells. We study analytically and numerically the stability of the cancer-free equilibrium and its dependence on the model parameters. We find that quiescent cells can escape the M-phase drug. The dynamics of the G(0) phase dictates the dynamics of cancer as a whole. Moreover, we find oscillations through a Hopf bifurcation. Finally, we use the model to discuss the efficiency of cell synchronization before treatment (synchronization method).
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada. wliu@math.ualberta.ca
Wenxiang
W
Liu
Thomas
T
Hillen
H I
HI
Freedman
D000818:Animals; D000970:Antineoplastic Agents / Q000008:administration & dosage*; D002453:Cell Cycle / Q000187:drug effects* / Q000276:immunology*; D003198:Computer Simulation; D006801:Humans; D007113:Immunity, Innate / Q000187:drug effects / Q000276:immunology*; D008954:Models, Biological; D009369:Neoplasms / Q000188:drug therapy* / Q000276:immunology* / Q000473:pathology
D000970:Antineoplastic Agents