A Policy to Eradicate Tumor in a Discrete-Continuous Immune Cell-Tumor Cell-Drug Administration Model with the Help of Stability Analysis and Bifurcation Analysis of the Model

Ranu Paul; Anusmita Das; Debashish Bhattacharya; Hemanta Kr. Sarmah

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A Policy to Eradicate Tumor in a Discrete-Continuous Immune Cell-Tumor Cell-Drug Administration Model with the Help of Stability Analysis and Bifurcation Analysis of the Model

机译：在模型的稳定性分析和分岔分析的帮助下，在离散连续免疫细胞 - 肿瘤细胞 - 药物管理模型中消除肿瘤的政策

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In this paper we have analyzed an immune cell-tumor cell model of Lotka-Voltera type with the control policy in the form of chemotherapy. We derived the conditions for the stability of the tumor free equilibrium point. Investigation regarding the possible bifurcation types was carried out for the system and it was observed that the system exhibits a transcritical bifurcation and undergoes period doubling route to chaos as the control parameter is varied. Combining the results of stability analysis and bifurcation analysis we determined a range for the rate of drug administration to eradicate the tumor completely. Numerical simulations were performed to observe the qualitative behaviour of the system as the control parameter is varied.

机译：在本文中，我们已经分析了Lotka-Voltera类型的免疫细胞 - 肿瘤细胞模型，并以化疗的形式进行了控制政策。我们衍生出肿瘤自由平衡点稳定性的条件。对系统进行了有关可能分叉类型的研究，并观察到该系统表现出跨临界分叉并且经历与对照参数变化的混沌的倍增途径。结合稳定性分析和分叉分析的结果，我们确定了药物管理速率的范围，以完全消除肿瘤。执行数值模拟以观察系统的定性行为，因为控制参数变化。

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来源
《International Journal of Applied Engineering Research》 |2019年第9期|共6页
作者
Ranu Paul; Anusmita Das; Debashish Bhattacharya; Hemanta Kr. Sarmah;
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作者单位

Department of Mathematics Gauhati University;

Department of Mathematics Gauhati University;

Department of Mathematics Gauhati University;

Department of Mathematics Gauhati University;

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原文格式 PDF
正文语种 eng
中图分类工程基础科学;
关键词
Lotka-Voltera type; Transcritical bifurcation; Period doubling route to chaos;

机译：Lotka-Volterra类型;跨临界分叉;周期加倍到混乱;

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1. A Policy to Eradicate Tumor in a Discrete-Continuous Immune Cell-Tumor Cell-Drug Administration Model with the Help of Stability Analysis and Bifurcation Analysis of the Model [J] . Ranu Paul, Anusmita Das, Debashish Bhattacharya, International Journal of Applied Engineering Research . 2019,第9期

机译：在模型的稳定性分析和分岔分析的帮助下，在离散连续免疫细胞 - 肿瘤细胞 - 药物管理模型中消除肿瘤的政策
2. Stability and bifurcation analysis of delay induced tumor immune interaction model [J] . Khajanchi Subhas, Banerjee Sandip Applied mathematics and computation . 2014,第Null期

机译：延迟诱导的肿瘤免疫相互作用模型的稳定性和分叉分析
3. Bifurcation analysis for a nonlinear system of integro-differential equations modelling tumor-immune cells competition [J] . Bellomo N., Guerri L., Firmani B. Applied mathematics letters . 1999,第2期

机译：非线性微分积分方程组的模型分析肿瘤免疫细胞竞争
4. BIFURCATIONS AND OSCILLATORY DYNAMICS IN A TUMOR IMMUNE INTERACTION MODEL [C] . SUBHAS KHAJANCHI International Symposium on Mathematical and Computational Biology . 2016

机译：肿瘤免疫相互作用模型中的分叉和振荡动力学
5. Vehicle handling, stability, and bifurcation analysis for nonlinear vehicle models. [D] . Nguyen, Vincent. 2005

机译：非线性车辆模型的车辆操纵，稳定性和分叉分析。
6. Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays [O] . Sid Visser, Hil GE Meijer, Michel JAM van Putten, 2012

机译：具有两个时滞的新皮层集总模型的不动点的稳定性和分岔以及周期解的分析
7. BIFURCATION ANALYSIS IN MODELS OF TUMOR AND IMMUNE SYSTEM INTERACTIONS [O] . Dan Liu, Shigui Ruan, Deming Zhu 2014

机译：肿瘤与免疫系统相互作用模型的分岔分析

A Policy to Eradicate Tumor in a Discrete-Continuous Immune Cell-Tumor Cell-Drug Administration Model with the Help of Stability Analysis and Bifurcation Analysis of the Model

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