Scholarlink

<p>Cancer attracts significant attention nowadays due to its rising global incidence, the complexity of its biological mechanisms, and the challenges it presents in treatment and prevention. In this context, a mathematical model provides a powerful tool for understanding this critical aspect of cancer biology. This paper introduces a novel, comprehensive mathematical model that looks into the intricate interactions between cancer cells, immune cells, cytokines, and the extracellular matrix. We derive biologically feasible equilibria and examine both local and global stability. Using Sotomayor’s theorem, the occurrence of saddle-node bifurcation is established, and the Hopf bifurcation is thoroughly analyzed. We investigate codimension-2 bifurcations, such as the Bogdanov-Takens bifurcation, using normal form theory and the center manifold theorem. Furthermore, an uncertainty analysis utilizing Latin hypercube sampling is performed to evaluate the influence of parameter uncertainties on tumor growth, which is then followed by a sensitivity analysis. The model incorporates multiplicative white noise terms into the deterministic system to construct a stochastic framework. Then we identify the sufficient conditions for mean persistence and extinction for every variable. Finally, numerical simulations are conducted by adjusting the parameters to confirm the analytical findings, providing new perspectives on controlling tumor behavior.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On investigation of complexity in extracellular matrix-induced cancer dynamics under deterministic and stochastic framework

  • 期刊论文

  • 发表日期：

    2025年1月17日

查看全文
  • Ranjit Kumar Upadhyay,
  • Amit Kumar Barman,
  • Parthasakha Das,
  • Binay Panda

摘要

Cancer attracts significant attention nowadays due to its rising global incidence, the complexity of its biological mechanisms, and the challenges it presents in treatment and prevention. In this context, a mathematical model provides a powerful tool for understanding this critical aspect of cancer biology. This paper introduces a novel, comprehensive mathematical model that looks into the intricate interactions between cancer cells, immune cells, cytokines, and the extracellular matrix. We derive biologically feasible equilibria and examine both local and global stability. Using Sotomayor’s theorem, the occurrence of saddle-node bifurcation is established, and the Hopf bifurcation is thoroughly analyzed. We investigate codimension-2 bifurcations, such as the Bogdanov-Takens bifurcation, using normal form theory and the center manifold theorem. Furthermore, an uncertainty analysis utilizing Latin hypercube sampling is performed to evaluate the influence of parameter uncertainties on tumor growth, which is then followed by a sensitivity analysis. The model incorporates multiplicative white noise terms into the deterministic system to construct a stochastic framework. Then we identify the sufficient conditions for mean persistence and extinction for every variable. Finally, numerical simulations are conducted by adjusting the parameters to confirm the analytical findings, providing new perspectives on controlling tumor behavior.