Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes.

IF 4.1 3区数学 Q1 Mathematics

Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-10-26 DOI:10.1186/s13662-021-03621-4

Kaushik Dehingia, Hemanta Kumar Sarmah, Yamen Alharbi, Kamyar Hosseini

引用次数: 0

Abstract

In this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to analyze and observe the dynamics of the model along with variation of vital parameters and the delay effect on anti-tumor immune responses. We obtain sufficient conditions for the existence of equilibrium points and their stability. Existence of Hopf bifurcation at co-axial equilibrium is investigated. The stability of bifurcating periodic solutions is discussed, and the time length for which the solutions preserve the stability is estimated. Furthermore, we have derived the conditions for the direction of bifurcating periodic solutions. Theoretically, it was observed that the system undergoes different states if we vary the system's parameters. Some numerical simulations are presented to verify the obtained mathematical results.

Abstract Image

查看原文本刊更多论文

对肿瘤与免疫相互作用和刺激过程中存在时间延迟的癌症模型进行数学分析。

在本研究中，我们讨论了在肿瘤与免疫相互作用和刺激过程中考虑离散时间延迟的癌症模型。本研究旨在分析和观察该模型随着重要参数的变化而产生的动态变化，以及延迟对抗肿瘤免疫反应的影响。我们获得了平衡点存在及其稳定性的充分条件。研究了共轴平衡点上霍普夫分岔的存在性。讨论了分岔周期解的稳定性，并估算了解保持稳定的时间长度。此外，我们还推导出了分岔周期解方向的条件。从理论上观察到，如果我们改变系统的参数，系统会经历不同的状态。为了验证所获得的数学结果，我们进行了一些数值模拟。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Advances in Difference Equations 数学-数学

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.