We propose a new mathematical model of erythropoiesis that takes a positive feedback of erythrocytes on progenitor apoptosis into account, and incorporates a negative feedback of erythrocytes on progenitor self-renewal. The resulting model is a system of age-structured equations that reduces to a system of delay differential equations where the delays account for progenitor compartment duration and cell cycle length. We compare this model with experimental data on an induced-anemia in mice that exhibit damped oscillations of the hematocrit before it returns to equilibrium. When we assume no self-renewal of progenitors, we obtain an inaccurate fitting of the model with experimental data. Adding self-renewal in the progenitor compartment gives better approximations, with the main features of experimental data correctly fitted. Our results indicate the importance of progenitor self-renewal in the modelling of erythropoiesis. Moreover, the model makes testable predictions on the lifespan of erythrocytes confronted to a severe anemia, and on the progenitors behavior.