Diffusion modeling of tumor-CD4$ ^+ $-cytokine interactions with treatments: Asymptotic behavior and stationary patterns
Diffusion modeling of tumor-CD4$ ^+ $-cytokine interactions with treatments: Asymptotic behavior and stationary patterns
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DOI：
10.3934/dcdsb.2021090
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Wenbin Yang;Yujing Gao;Xiaojuan Wang
中科院分区：
文献类型：
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作者：
Wenbin Yang;Yujing Gao;Xiaojuan Wang
在这项工作中，我们考虑了一个扩散的肿瘤-CD 4\开始{document}$ ^+ $\end{document} -细胞因子相互作用模型与免疫治疗下齐次Neumann边界条件。我们首先研究了非负平衡点的长时间行为，包括系统的持续生存和稳定性条件。我们还给出了非常数正稳态的存在性（即，静止图案），这表明该静止图案是由扩散效应驱动的。在本研究中，我们使用抛物型系统的比较原理，线性化方法，能量积分方法和Leray-Schauder度。
In this work, we consider a diffusive tumor-CD4 \begin{document}$ ^+ $\end{document} -cytokine interactions model with immunotherapy under homogeneous Neumann boundary conditions. We first investigate the large-time behavior of nonnegative equilibria, including the system persistence and the stability conditions. We also give the existence of nonconstant positive steady states (i.e., a stationary pattern), which indicate that this stationary pattern is driven by diffusion effects. For this study, we employ the comparison principle for parabolic systems, linearization method, the method of energy integral and the Leray-Schauder degree.