Cancer treatment by stem cells and chemotherapy as a mathematical model with numerical simulations

Alqudah, Manar A.

doi:10.1016/j.aej.2019.12.025

Cited by 31 publications

(16 citation statements)

References 20 publications

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“…As in [13,14,15,16] the effectiveness of using stem cells to boost the patient's immune system has been shown, which may in the future be a treatment for most types of cancer. In this work, we extend the study [17]. Taking into account the interaction of stem cells, tumor cells and chemotherapy for the treatment of cancer, we propose a fractional-order instead of integer-order model to show how effective stem cells are in improving the immune system, which in turn better fights tumor cells [10,11,12,18].…”

Section: Introductionmentioning

confidence: 95%

“…heat equation, telegraph equation, social systems, medical imaging, pollution control, cancer dynamics, infectious diseases, and a lossy electric transmission line are all involved with fractional order operators [8,9,18,19]. We propose a model motivated by Manar A. Alqudah's work [17], Manar presented a study of ordinary differential equations model that describes the stem cells and chemotherapy for treatment of cancer to show how the stem cells support the effector cells which fighting the tumor cells to improve the immune system of the cancer patient while the chemotherapy kills the infected cells. The mathematical model of treatment of cancer studied in [17] is presented by:…”

Section: Introductionmentioning

confidence: 99%

“…We propose a model motivated by Manar A. Alqudah's work [17], Manar presented a study of ordinary differential equations model that describes the stem cells and chemotherapy for treatment of cancer to show how the stem cells support the effector cells which fighting the tumor cells to improve the immune system of the cancer patient while the chemotherapy kills the infected cells. The mathematical model of treatment of cancer studied in [17] is presented by:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fractional-order mathematical modelling of cancer cells-cancer stem cells-immune system interaction with chemotherapy

Özköse¹,

Şenel²,

Habbireeh³

2021

mmnsa

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In this paper, we present a mathematical model of stem cells and chemotherapy for cancer treatment, in which the model is represented by fractional order differential equations. Local stability of equilibrium points is discussed. Then, the existence and uniqueness of the solution are studied. In addition, in order to point out the advantages of the fractional order modeling, the memory trace and hereditary traits are taken into consideration. Numerical simulations have been used to investigate how the fractional order derivative and different parameters affect the population dynamics, the graphs have been illustrated according to different values of fractional order α and different parameter values. Moreover, we have examined the effect of chemotherapy on tumor cells and stem cells over time. Furthermore, we concluded that the memory effect occurs as the α decreases from 1 and the chemotherapy drug is quite effective on the populations. We hope that this work will contribute to helping medical scientists take the necessary measures during the screening process and treatment.

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractional-order mathematical modelling of cancer cells-cancer stem cells-immune system interaction with chemotherapy

Özköse¹,

Şenel²,

Habbireeh³

2021

mmnsa

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“…In [24], the authors presented a model for the growth of the immune system during chemotherapy. Alqudah [25] introduced a new mathematical model for the treatment of cancer as a combination of chemotherapy and stem cell therapy.…”

Section: Introductionmentioning

confidence: 99%

An Optimal Control Problem of Chemotherapy In Presence of Gene and Immunotherapy

Dehingia¹

2021

Preprint

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In this study, a cancer eradication model involving effector cells in the presence of gene therapy, immunotherapy, and chemotherapy has been proposed. Boundedness and positiveness of the solutions in the respective feasible domains of the proposed model are verified. Conditions for which the equilibrium points of the system are stable have been derived. Amounts of immunotherapy to be injected to a patient for eradication of cancerous tumor cells have been found. To minimize the chemotherapy drug-induced toxicity to the patient, an optimal control problem for the system has been constructed and solved. Numerical and graphical results have been presented. Through the investigation, it was seen that tumor cells can be eliminated in a specific time interval with the control of chemotherapeutic drug concentration.

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“…Moreover, in the context of thermostatted kinetic theory, the correlations between the immune system and a tumor are defined at cell scales [22]. Ordinary differential equations (ODEs) [23][24][25], partial differential equations (PDEs) [26,27], and delay differential equations (DDEs) [28,29] have been used to suggest cancer models and study the effects of tumor growth on the dynamics of other cells or dynamics of brain diseases [30].…”

Section: Introductionmentioning

confidence: 99%

A New ODE-Based Model for Tumor Cells and Immune System Competition

Alharbi

Rambely

2020

Mathematics

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Changes in diet are heavily associated with high mortality rates in several types of cancer. In this paper, a new mathematical model of tumor cells growth is established to dynamically demonstrate the effects of abnormal cell progression on the cells affected by the tumor in terms of the immune system’s functionality and normal cells’ dynamic growth. This model is called the normal-tumor-immune-unhealthy diet model (NTIUNHDM) and governed by a system of ordinary differential equations. In the NTIUNHDM, there are three main populations normal cells, tumor cell and immune cells. The model is discussed analytically and numerically by utilizing a fourth-order Runge–Kutta method. The dynamic behavior of the NTIUNHDM is discussed by analyzing the stability of the system at various equilibrium points and the Mathematica software is used to simulate the model. From analysis and simulation of the NTIUNHDM, it can be deduced that instability of the response stage, due to a weak immune system, is classified as one of the main reasons for the coexistence of abnormal cells and normal cells. Additionally, it is obvious that the NTIUNHDM has only one stable case when abnormal cells begin progressing into early stages of tumor cells such that the immune cells are generated once. Thus, early boosting of the immune system might contribute to reducing the risk of cancer.

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Cancer treatment by stem cells and chemotherapy as a mathematical model with numerical simulations

Cited by 31 publications

References 20 publications

Fractional-order mathematical modelling of cancer cells-cancer stem cells-immune system interaction with chemotherapy

Fractional-order mathematical modelling of cancer cells-cancer stem cells-immune system interaction with chemotherapy

An Optimal Control Problem of Chemotherapy In Presence of Gene and Immunotherapy

A New ODE-Based Model for Tumor Cells and Immune System Competition

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