溶瘤治疗模型中交叉扩散诱导的图灵分岔和振幅方程:病毒作为抗肿瘤手段

F. Najm, R. Yafia, M. Aziz-Alaoui
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引用次数: 0

摘要

在本文中,我们提出了一个在二维域上增加自扩散/交叉扩散的反应扩散数学模型,该模型描述了肿瘤的生长遵循logistic规律的溶瘤病毒治疗。肿瘤细胞分为未感染细胞和感染细胞,病毒传播应该是直接模式(从细胞到细胞)。在没有交叉扩散的情况下,我们建立了问题的适定性、解的非负性和有界性、正解的不存在性、非平凡稳态的局部稳定性和全局稳定性以及图灵不稳定性的不发生性。在交叉扩散存在的情况下,我们用感染细胞的交叉扩散系数作为参数证明了图灵不稳定性的存在。为了了解不同的模式,我们利用非线性分析理论推导出相应的振幅方程。最后,对所得理论结果进行了数值模拟。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Turing Bifurcation Induced by Cross-Diffusion and Amplitude Equation in Oncolytic Therapeutic Model: Viruses as Anti-Tumor Means
In this paper, we propose a reaction–diffusion mathematical model augmented with self/cross-diffusion in 2D domain which describes the oncolytic virotherapy treatment of a tumor with its growth following the logistic law. The tumor cells are divided into uninfected and infected cells and the virus transmission is supposed to be in a direct mode (from cell to cell). In the absence of cross-diffusion, we establish well posedness of the problem, non-negativity and boundedness of solutions, nonexistence of positive solutions, local and global stability of the nontrivial steady-state and the nonoccurrence of Turing instability. In the presence of cross-diffusion, we prove the occurrence of Turing instability by using the cross-diffusion coefficient of infected cells as a parameter. To have an idea about different patterns, we derive the corresponding amplitude equation by using the nonlinear analysis theory. In the end, we perform some numerical simulations to illustrate the obtained theoretical results.
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