Asymptotic analysis of mathematical model describing a new treatment of breast cancer using AZD9496 and palbociclib - Nave, Ophir (Frontiers in Oncology, 2025)
IntroductionCancer is a collective name for a group of diseases consisting of dozens of different types of malignant tumors, characterized by rapid and uncontrolled proliferation of cells in the body. Cancer can start almost anywhere in the human body such as the breast, prostate, colorectal, brain, bones, lungs, bladder etc. The main differences between the different types of cancer are related to the organ in which the tumor develops and the type of cells that compose the tumor.MethodThis paper focused on the breast cancer. Breast cancer is a malignant tumor that originates in the breast tissue. It is the most common malignant tumor in women. There are several types of breast cancer, but in all types early diagnosis and treatment is crucial. In this study, the treatment of breast cancer involving a combination of two drugs was investigated: the oral estrogen receptor inhibitor AZD9496 and the CDK4/6 protein inhibitor Palbociclib. The mathematical model that described the interaction between the cancer cells, the treatment, and the immune system cells includes a system of nonlinear ordinary differential equations of the firs order. In general, dynamic variables of a given system change each at a different rate. And it is not possible to know from the mathematical model which variable is fast and which is slow. Therefore, in order to reveal the hierarchy of the system of equations ,a numerical algorithm called the singularly perturbed vector field (SPVF) was applied. This algorithm transform the mathematical model to a new coordinate system in which the rate of change of each dynamic variable of the system can be known.Results and DiscussionAfter writing the mathematical model in new coordinates, the equilibrium point was obtained analytically. The stability of the equilibrium points is investigated, which is essential from a practical perspective. Investigating the stability of the equilibrium points allows determination of when the tumor does not continue to develop and thereby allows adjustment of treatment continuation.