The in vivo erythropoiesis, which is the generation of mature red blood cells in the bone marrowof whole organisms,has been described by a variety of mathematical models in the past decades. However, the in vitro erythropoiesis, whichproduces red blood cells in cultures, has received much less attention from the modelling community. In this paper, wepropose the first mathematical model of in vitro erythropoiesis. We start by formulating different models and select the bestone at fitting experimental data of in vitro erythropoietic differentiation obtained from chicken erythroid progenitor cells. Itis based on a set of linear ODE, describing 3 hypothetical populations of cells at different stages of differentiation. We thencompute confidence intervals for all of its parameters estimates, and conclude that our model is fully identifiable. Finally,we use this model to compute the effect of a chemical drug called Rapamycin, which affects all states of differentiation inthe culture, and relate these effects to specific parameter variations. We provide the first model for the kinetics of in vitrocellular differentiation which is proven to be identifiable. It will serve as a basis for a model which will better account for thevariability which is inherent to the experimental protocol used for the model calibration.