In this paper, we have elaborated an analytical model to study the dynamics of the Smof-Lipid delivery in Neonate nutrition fluid with an Intravenous (IV) infusion system. For a simple configuration, containing two inlets and one outlet, used mainly in neonatology, analytical computations were performed in order to study the impact of different factors such as: the common dead volume (V), the cessation of the drug infusion and the variation of the carrier flow-rate on the dynamics of the drug delivery. The influence of the viscosity of different fluids used in the study on the head losses in all branches of the IV system as well as on the variation of the pressure at the inlets of the infusion system has been investigated as well. In a first step, the analytical model was validated for the steady-state administrated drug concentration with some analytical results existed in the literature [1]. In the second part, the influence of the common dead-volume (V) on the Smof-Lipid administration with constant carrier and drug flow-rates and respectively, has been investigated for 250min of drug administration before proceeding a cessation. Different results illustrate that the achievement of the drug steady-state administration depends strongly on the common dead volume (V) of the mixing compartment. It’s determined that, for the fixed carrier and drug flow-rates cited above, going from V = 0.5ml to V = 1ml by adding an extension tubing to the catheter could provoke a lag of about 60min instead of 28min to reach the steady-state concentration. This time could be longer (almost 124min) if the common dead volume is increased up to V = 2ml. After that, fixing the common dead-volume at V = 1ml, the impact of the cessation of the drug infusion on the evolution of the administered Smof-lipid concentration has been studied in function with the variation of the carrier flow-rate after the cessation phase. It has proved that an increasing in the carrier flow-rate provokes an acceleration of the elimination of the smof-lipid quantity contained in the dead-volume. Contrary, a decreasing in the carrier flow-rate causes further delay to achieve a complete elimination of the drug in the dead-volume. It’s also depicted that fixing the flow conditions, the head loss in different branches of the IV system depends principally on the viscosity of the fluid passing through, and the higher is the fluid viscosity, the more head loss is generated.