A general class of hybrid models has been introduced recently, gathering the advantages multiscale descriptions. Concerning biological applications, the particular coupled structure fits to collective cell migrations and pattern formation scenarios. In this context, cells are modelled as discrete entities and their dynamics is given by ODEs, while the chemical signal influencing the motion is considered as a continuous signal which solves a diffusive equation. From the analytical point of view, this class of model has been proved to have a mean-field limit in the Wasserstein distance towards a system given by the coupling of a Vlasov-type equation with the chemoattractant equation. Moreover, a pressureless nonlocal Euler-type system has been derived for these models, rigorously equivalent to the Vlasov one for monokinetic initial data. In the present paper, we present a numerical study of the solutions to the Vlasov and Euler systems, exploring general settings for inital data, far from the monokinetic ones.

翻译：近期引入了一类通用的混合模型，融合了多尺度描述的优势。在生物学应用中，这种特殊的耦合结构适用于集体细胞迁移和模式形成场景。在此背景下，细胞被建模为离散实体，其动力学由常微分方程描述，而影响运动的化学信号则被视为连续信号，并满足扩散方程。从分析角度看，这类模型已被证明在Wasserstein距离下具有平均场极限，可收敛至由Vlasov型方程与化学吸引物方程耦合组成的系统。此外，针对这些模型推导出无压力的非局部Euler型系统，该模型对于单动初始数据严格等价于Vlasov模型。本文对Vlasov和Euler系统的解开展了数值研究，探讨了远离单动初始条件的通用初始数据设置。