Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model

Kemal Türk; Mehmet Gümüş

doi:10.33401/fujma.1696954

Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model

Abstract

Cancer is a major health problem worldwide. Mathematical models play a critical role in understanding the spread of the disease and the effects of treatment. In this study, a discrete version of a cancer model is developed using the Euler method. The conditions necessary for the discretized model's solutions to be non-negative and bounded are obtained. Six different equilibria are identified, and the feasibility conditions for these equilibria are established. Furthermore, the local asymptotic stability of each equilibrium is rigorously proved. Restrictions on the time-step size $h$ were derived to ensure the validity of the results, and simulations were performed to verify the stability behavior and the influence of the time-step size. The study established essential conditions for the discretization of mathematical models so as to preserve biological relevance and dynamical consistency. Moreover, the discrete formulation offers a flexible framework for the computational analysis of cancer dynamics and has the potential to inform future research directions.

Keywords

References

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Details

Primary Language

English

Subjects

Biological Mathematics

Journal Section

Research Article

Authors

Kemal Türk
0000-0003-4079-4207
Türkiye

Mehmet Gümüş ^*
0000-0002-7447-479X
Türkiye

Publication Date

September 30, 2025

Submission Date

May 10, 2025

Acceptance Date

September 28, 2025

Published in Issue

Year 2025 Volume: 8 Number: 3

DOI

https://doi.org/10.33401/fujma.1696954

IZ

https://izlik.org/JA63RD62NP

Cite

RIS / Bibtex

APA

Türk, K., & Gümüş, M. (2025). Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model. Fundamental Journal of Mathematics and Applications, 8(3), 148-160. https://doi.org/10.33401/fujma.1696954

AMA

1.Türk K, Gümüş M. Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model. Fundam. J. Math. Appl. 2025;8(3):148-160. doi:10.33401/fujma.1696954

Chicago

Türk, Kemal, and Mehmet Gümüş. 2025. “Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model”. Fundamental Journal of Mathematics and Applications 8 (3): 148-60. https://doi.org/10.33401/fujma.1696954.

EndNote

Türk K, Gümüş M (September 1, 2025) Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model. Fundamental Journal of Mathematics and Applications 8 3 148–160.

IEEE

[1]K. Türk and M. Gümüş, “Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model”, Fundam. J. Math. Appl., vol. 8, no. 3, pp. 148–160, Sept. 2025, doi: 10.33401/fujma.1696954.

ISNAD

Türk, Kemal - Gümüş, Mehmet. “Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model”. Fundamental Journal of Mathematics and Applications 8/3 (September 1, 2025): 148-160. https://doi.org/10.33401/fujma.1696954.

JAMA

1.Türk K, Gümüş M. Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model. Fundam. J. Math. Appl. 2025;8:148–160.

MLA

Türk, Kemal, and Mehmet Gümüş. “Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model”. Fundamental Journal of Mathematics and Applications, vol. 8, no. 3, Sept. 2025, pp. 148-60, doi:10.33401/fujma.1696954.

Vancouver

1.Kemal Türk, Mehmet Gümüş. Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model. Fundam. J. Math. Appl. 2025 Sep. 1;8(3):148-60. doi:10.33401/fujma.1696954