Tumor-Immune Interaction System with the Effect of Time Delay and Hyperglycemia on the Breast Cancer Cells

Alblowy, Abeer Hamdan; Maan, Normah; Awang, Nor Aziran

doi:10.4236/jamp.2023.114076

Cited by 2 publications

(1 citation statement)

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“…Many mathematical works have been performed to capture some key features of the dynamics of breast cancer cells [5,6]. However, there are still many challenges, such as the complex interactions between cancer cells and the immune system and cancer's genetic and molecular characteristics, to be addressed in breast cancer modelling [7,8]. Enderling et al [9] analyzed a breast cancer model to comprehend its development and the impact of various cancer-curing treatment modalities, identify different sources of local recurrence, and examine their prevention.…”

Section: Introductionmentioning

confidence: 99%

A study on the dynamics of a breast cancer model with discrete-time delay

Das,

Dehingia,

Hinçal

et al. 2024

Phys. Scr.

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This study aims to discuss the impact of discrete-time delay on the anti-tumor immune response against tumor growth, excess levels of estrogen, and the source rate of immune cells in a breast cancer model. The non-negativity and boundedness of the solutions of the model are discussed. The existence of equilibria and their stability are examined. It is found that if the estrogen level is normal and the source rate of immune cells is low, the stability of the model around the co-existing equilibrium switches to instability via a Hopf bifurcation as the time delay increases. To validate the theoretical findings, a few numerical examples have been presented. The main result of this study is that the growth of tumors can be controlled if the immune system quickly generates an anti-tumor immune response. However, if the immune system takes a longer time to generate anti-tumor immune responses, the tumor growth cannot be controlled, and the system becomes unstable, which may result in the further spread of the disease.

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