DEPARTMENT OF MATHEMATICAL AND STATISTICAL SCIENCES
UNIVERSITY OF ALBERTA

PIMS-MITACS MATHEMATICAL BIOLOGY SEMINAR


MONDAY, January 30, 2006
3:00 - 4:00 p.m.
CAB 657

Wenxiang Liu


A Mathematical Model for Cancer Treatment by Cell Cycle-Specific Chemotherapy.

In this paper we use a mathematical model to study the effect of a cell-cycle specific drug on the development of cancer, including the immune response. The cancer cells are split into the mitotic phase (M-phase), the quiescent phase (G0-phase) and the interphase (G1; S; G2 phases). We include a time delay for the passage through the interphase. The immune cells interact with all cells and the drug is assumed to be M-phase specific. We study analytically and numerically the stability of the cancer-free equilibrium and we show that the M-phase specific drug does not change its stability. Nevertheless, the M-phase drug significantly reduces cancer growth. Moreover we find oscillations through a Hopf bifurcation. Finally, we use the model to discuss the efficiency of cell synchronization before treatment (synchronization method).

Refreshments will be served following the seminar from 4:00 to 5:00 p.m. in CAB 549