A mathematical model for phase transition regulation on the cell cycle in early stage of breast cancer

Prameswari, Ken; Adi-Kusumo, Fajar

doi:10.1063/1.5139160

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…e gene mutations affect the cell cycle, DNA damages, and some anomalies on the cells. Some anomalies' behaviour of the enzymes in the cells due to the DNA damage caused by cancer has been shown in [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

“…In the subcellular level, the cancer infections are mainly caused by the gene mutation represented by the shifting concentration of the enzymes. ere are some enzymes that can be used as the indicators of the mutation, e.g., p53, pRb, and EBNA1; see [1][2][3]. For the breast cancer case, the gene mutations triggered by the enzyme reactions can cause anomalies on the cell cycle and cell repair regulations; see [2,3].…”

Section: Introductionmentioning

confidence: 99%

“…ere are some enzymes that can be used as the indicators of the mutation, e.g., p53, pRb, and EBNA1; see [1][2][3]. For the breast cancer case, the gene mutations triggered by the enzyme reactions can cause anomalies on the cell cycle and cell repair regulations; see [2,3]. e immunotherapy model of cancer that involves the interaction between the cancer cells, the effector cells, and the IL-2 compounds was motivated by Kirschner et al [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions

Suddin

Adi-Kusumo

Aryati

et al. 2021

International Journal of Differential Equations

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Immunotherapy is one of the future treatments applicable in most cases of cancer including malignant cancer. Malignant cancer usually prevents some genes, e.g., p53 and pRb, from controlling the activation of the cell division and the cell apoptosis. In this paper, we consider the interactions among the cancer cell population, the effector cell population that is a part of the immune system, and cytokines that can be used to stimulate the effector cells called the IL-2 compounds. These interactions depend on both time and spatial position of the cells in the tissue. Mathematically, the spatial movement of the cells is represented by the diffusion terms. We provide an analytical study for the constant equilibria of the reaction-diffusion system describing the above interactions, which show the initial behaviour of the tissue, and we conduct numerical simulation that shows the dynamics along the tissue that represent the immunotherapy effects. In this case, we also consider the steady-state conditions of the system that show the long-time behaviour of these interactions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions

Suddin

Adi-Kusumo

Aryati

et al. 2021

International Journal of Differential Equations

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“…Enderling et al in [7] modeled the breast cancer development, the local treatment, and the recurrence. Furthermore, Prameswari and Adi-Kusumo [8] constructed a model of the phase transition regulation on cell cycle to characterize breast cancer cells' growth in the earlier stage, which is indicated by the anomalies of cell proliferation. e model knows the behavior changes in cell concentration used as an early indicator of cancer growth.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Breast Cancer Model for Neutropenia Case due to Chemotherapy Effects

Fathoni

Adi-Kusumo

Gunardi

et al. 2021

International Journal of Differential Equations

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Breast cancer is a type of carcinoma with a high prevalence. The treatment of breast cancer through chemotherapy can cause a risk to healthy cells throughout the body. The neutrophil is one of the cells that is influenced by chemotherapy drugs. Chemotherapy-induced neutropenia is one of the most common toxic effects experienced by patients and often threatens chemotherapy to use efficiency. In this paper, we introduce an interaction model between blood components, i.e., neutrophil, lymphocytes, and albumin, with chemotherapy drugs. The model is important to understand the neutropenia effect due to chemotherapy in mathematical perspective and to calculate breast cancer patients’ survival level. Our model is a four-dimensional system of the first-order ODE with 13-dimensional parameter space. We focus our study for understanding the steady-state conditions and the bifurcations when the parameter values are varied. Here, we also study the role of albumin for reducing the neutropenia effects for breast cancer patients mathematically, where the results can be used as an alternative solution for treating neutropenia in a breast cancer case.

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A study on ODE-based model of risk breast cancer with body mass

Abdulkream Alharbi,

Dehingia,

Jahman Alqarni

et al. 2023

Applied Mathematics in Science and Engineering

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A mathematical model for phase transition regulation on the cell cycle in early stage of breast cancer

Cited by 3 publications

References 18 publications

Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions

Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions

Dynamics of a Breast Cancer Model for Neutropenia Case due to Chemotherapy Effects

A study on ODE-based model of risk breast cancer with body mass

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