Fractional-Order Mathematical Modeling and Stability Analysis of Tumor-Immune System Relation Including Chemotherapy Drug Effect

Esen Kaya; Fatma Özköse; M. Tamer Senel

doi:10.29002/asujse.1384833

TR EN

Kemoterapi İlaç Etkisi Dahil Tümör-Bağışıklık Sistemi İlişkisinin Kesirli Mertebeden Matematiksel Modellenmesi ve Kararlılık Analizi

Öz

Kanser dünya çapında ikinci en sık ölüm nedenidir. Kemoterapi, özellikle kanserli tümörlerin büyümesinin ve boyutlarının kontrol edilmesinde etkili olan, tümör tedavisinde yaygın olarak kullanılan bir stratejidir. Kemoterapi mekanizmalarının karmaşıklığının daha derinlemesine anlaşılmasını sağlamak için kemoterapi varlığında tümör büyümesini gösteren kesirli dereceli bir matematiksel model oluşturduk. Bu her şeyi kapsayan paradigma, hem ilaç tedavisinin etkilerini hem de bağışıklık sisteminin tepkisini ele alır. Sistemin biyolojik önemini ortaya koymak için çözümlerin varlığına ve tekliğine bakarak çözümlerin pozitifliğini ve sınırlılığını ortaya koyduk. Yaklaşımımız, bu diferansiyel denklem modelinin dinamik özelliklerini karakterize etmek için denge noktalarının belirlenmesini ve bir dizi model parametresi dahilinde stabilite gereksinimlerinin araştırılmasını içerir. Ek olarak çeşitli parametre değerleriyle sayısal simülasyonlar yürüttük. Kesirli türevin hafıza etkisini göstermek için, ayrıca kesirli türevlerin çeşitli dereceleri için sistemin dinamik davranışını da simüle ettik. Başka bir deyişle, kemoterapötik tedavinin popülasyonlar üzerinde oldukça etkili olduğu ve hafıza etkisinin ϑ, 1'den düştüğünde ortaya çıktığı sonucuna vardık. Bu araştırmanın amacı, kanseri tedavi etmek ve teşhis koyarken uygun güvenlik önlemlerini alma konusunda hekimlere yardımcı olmaktır.

Anahtar Kelimeler

Fractional-Order Mathematical Modeling and Stability Analysis of Tumor-Immune System Relation Including Chemotherapy Drug Effect

Abstract

Worldwide, cancer is the second most common cause of death. Chemotherapy is a widely used strategy to tumor treatment that is particularly effective in controlling the growth of cancerous tumors and their size. We created a fractional-order mathematical model that illustrates tumor growth in the presence of chemotherapy to obtain a more profound comprehension of the complexities of chemotherapy mechanisms. This all-inclusive paradigm addresses both the impacts of medication therapy and the immune system's reaction. We demonstrated the positivity and boundedness of the solutions by looking at their existence and uniqueness in order to demonstrate the biological significance of the system. Our approach involves identifying equilibrium points and investigating stability requirements within a range of model parameters in order to characterize the dynamic features of this differential equation model. Additionally, we ran numerical simulations with various parameter values. To illustrate the memory effect of the fractional derivative, we also simulated the system's dynamic behavior for various orders of fractional derivatives. To put it another way, we came to the conclusion that the chemotherapeutic treatment is quite effective on populations and that the memory effect happens when ϑ, decreases from 1. The purpose of this research is to assist physicians in adopting the appropriate safety measures when diagnosing and treating cancer.

Keywords

Supporting Institution

Erciyes Üniversitesi

References

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Details

Primary Language

English

Subjects

Numerical Analysis

Journal Section

Research Article

Authors

Esen Kaya
0000-0002-4613-1722
Türkiye

Fatma Özköse ^*
0000-0002-7021-8342
Türkiye

M. Tamer Senel
0000-0003-1915-5697
Türkiye

Publication Date

December 30, 2024

Submission Date

November 1, 2023

Acceptance Date

November 1, 2024

Published in Issue

Year 2024 Volume: 8 Number: 2

DOI

https://doi.org/10.29002/asujse.1384833

IZ

https://izlik.org/JA45MK79RM

Cite

RIS / Bibtex

APA

Kaya, E., Özköse, F., & Senel, M. T. (2024). Fractional-Order Mathematical Modeling and Stability Analysis of Tumor-Immune System Relation Including Chemotherapy Drug Effect. Aksaray University Journal of Science and Engineering, 8(2), 85-101. https://doi.org/10.29002/asujse.1384833