We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding tissue. Transitions between the two cell subpopulations are influenced by subcellular (receptor binding) dynamics, thus conferring the setting a multiscale character.We prove global existence of weak solutions to a simplified model version and perform numerical simulations for the full setting under several phenotype switching and motility scenarios. We also compare (via simulations) this model with the corresponding haptotaxis-chemotaxis one featuring indirect chemorepellent production and provide a discussion about possible model extensions and mathematical challenges.

中文翻译：

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模拟多个出租车：具有表型异质性，触觉感和单侧种间排斥的肿瘤侵袭

我们简要回顾了（至少）一个物种执行的具有多个滑行的现有模型，并考虑了一种具有两种互斥的细胞表型（迁移和增殖）的新的肿瘤侵袭数学模型。迁移的细胞会响应非扩散线索而执行非线性扩散和两种滑行：远离增殖细胞并向上扩散周围组织。两个细胞亚群之间的转变受亚细胞（受体结合）动力学的影响，因此赋予了多尺度特征设置。场景。