We are interested in the system of ion channels present at the membrane of the human red blood cell. The cell, under specific experimental circumstances, presents important variations of its membrane potential coupled to variations of the main ions' concentration ensuring its homeostasis. In this collaborative work between biologists and mathematicians a simple mathematical model is designed to explain experimental measurements of membrane potential and ion concentrations. Its construction is presented, as well as illustrative simulations and a calibration of the model on real data measurements. A sensitivity analysis of the model parameters is performed. The impact of blood sample storage on ion permeabilities is discussed.