Research Article
Dynamics of a Breast Cancer Model for Neutropenia Case due to
Chemotherapy Effects
M. Ivan Ariful Fathoni ,
1,2
Fajar Adi-Kusumo ,
1
Gunardi Gunardi,
1
and Susanna Hilda Hutajulu
3
1
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia
2
Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Nahdlatul Ulama Sunan Giri,
Bojonegoro, Indonesia
3
Department of Internal Medicine, Faculty of Medicine, Public Health, and Nursing, Universitas Gadjah Mada,
Dr. Sardjito General Hospital, Yogyakarta, Indonesia
Correspondence should be addressed to Fajar Adi-Kusumo; f_adikusumo@ugm.ac.id
Received 24 July 2021; Accepted 29 September 2021; Published 20 October 2021
Academic Editor: Jianshe Yu
Copyright © 2021 M. Ivan Ariful Fathoni et al. is is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Breast cancer is a type of carcinoma with a high prevalence. e treatment of breast cancer through chemotherapy can cause a risk to
healthy cells throughout the body. e 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. e 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.
1. Introduction
Breast cancer is a type of a high prevalence carcinoma. It can
occur in both men and women, where the higher prevalence
is in women. Data from WHO in 2018 showed that the
number of new breast cancer cases was 2,088,849 or 11.6% of
the world’s total number of cancer cases. is number is only
different from 5,027 cases of lung cancer, which occupies the
first position. Based on this number, 626,679 of them were
the death cases. Asia is in the top rank of the number of
breast cancer incidence and mortality in the world [1]. e
disease is treatable if it is detected earlier and is still in its
earler stages. e higher the stage implies, the smaller the life
expectancy is. ere is no cancer that has a 100% mortality
rate; it means that the treatment can be done to get a cure,
especially if treatment is started earlier [2].
ere are several studies being carried out in cancer
modeling and treatment. Sch¨ attler et al. [3] developed a
mathematical model with minimal parameters for low-dose
metronomic chemotherapy. e model takes into account
the angiogenic signaling between the tumor and the vas-
culature and the tumor inhibitory effects of tumor-immune
system interactions. Liu and Yang [4] developed a cancer
treatment model with radiotherapy followed by chemo-
therapy. Jordão and Tavares [5] studied the dynamics of
healthy and diseased cells. e model for healthy cells is
based on the p53 gene network, cell cycle control mecha-
nism, the MAP kinase pathway, and the PI3K or Akt
pathway, a cancer cell model embodied by deregulation in a
healthy cell model. Solis-Perez et al. in [6] created a
mathematical model that considers the population dynamics
among cancer stem cells, tumor cells, healthy cells, the effects
of excess estrogen, and the body’s natural immune response
to cell populations.
Several mathematical models that are more specific to
breast cancer have been introduced before. Enderling
Hindawi
International Journal of Differential Equations
Volume 2021, Article ID 3401639, 8 pages
https://doi.org/10.1155/2021/3401639