quiescent depending of their positions, ages, …To study the influence of these diverse cells on each others from a theoretical view, we introduce mathematical model for multiple populations. In this paper we are interesting in the global dynamics and interactions of the two populations, meaning that we focus specifically on continuous models.

In the already existing literature on macroscopic model, we distinguish two categories. The most common ones involved partial differential equations (PDE) in which cells are represented by densities. These models have been widely used to model growth of tissue [@BD; @RBEJPJ], in particular for tumor growth [@AM04; @BCGRS; @Byrne; @BenAmar]. Another way to model tissue growth is by considering free boundary models [@Cui; @FriedmanHu; @Greenspan]. In these models the tissue is described by a domain and its growth and movement are driven by the motion of the boundary. The link between these two types of model has been been made via an incompressible limit in [@HV; @KimPozar; @MPQ; @PQTV; @PQV; @PV]. This link is interesting as both models have their advantages. On the one hand PDE relying models, also called mechanical models, are widely studied with many numerical and analytical tools. On the other hand free boundary models 