Scholarlink

<p>This study presents an extended mathematical model that can explain the intricate relationship between tumor carcinogenesis and macrophage activation as factors that promote cancer. The major goal is to investigate how macrophage concentration affects tumor growth and cancer development. In Caputo sense, the fractal-fractional derivative is used to accurately capture the dynamic behavior of macrophage-tumor responses. In connection with the fractal-fractional derivative, the solutions’ dynamical and stability behaviors are investigated. Additionally, we have examined the purposed models’ parameters with a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2310_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(\pm 10\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>±</mo> <mn>10</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> perturbation to determine their sensitivity. We validate analytical results and confirm the existence and uniqueness of fractal-fractional derivative solutions through numerical simulations. The results show that macrophages are also involved in the promotion of cancer and tumor growth. The results highlight the delicate balance between macrophage pro- and anti-tumor effects, which may help identify potential treatment targets. This work establishes the foundation for future research on cancer treatments and advances our knowledge of the interactions between the immune system and tumors. Python programs are used for graphic illustration.</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

The dynamic interactions between tumor carcinogenesis and macrophage activation: an extended mathematical model

  • 期刊论文

  • 发表日期：

    2025年4月7日

查看全文
  • Khadija Tul Kubra,
  • Samra Gulshan,
  • Rooh Ali

摘要

This study presents an extended mathematical model that can explain the intricate relationship between tumor carcinogenesis and macrophage activation as factors that promote cancer. The major goal is to investigate how macrophage concentration affects tumor growth and cancer development. In Caputo sense, the fractal-fractional derivative is used to accurately capture the dynamic behavior of macrophage-tumor responses. In connection with the fractal-fractional derivative, the solutions’ dynamical and stability behaviors are investigated. Additionally, we have examined the purposed models’ parameters with a \(\pm 10\%\) ± 10 % perturbation to determine their sensitivity. We validate analytical results and confirm the existence and uniqueness of fractal-fractional derivative solutions through numerical simulations. The results show that macrophages are also involved in the promotion of cancer and tumor growth. The results highlight the delicate balance between macrophage pro- and anti-tumor effects, which may help identify potential treatment targets. This work establishes the foundation for future research on cancer treatments and advances our knowledge of the interactions between the immune system and tumors. Python programs are used for graphic illustration.