The use of a hood to administer therapeutic aerosols to wheezy infants has many advantages and was found as efficient as administration using a mask. The aim of the present study is to investigate numerically the airflow induced drug dispersion inside the hood. Drug droplet dispersion is examined with respect to three breathing phases: inspiration, expiration, and apnea. The governing equations describing the airflow and the trajectories of drug droplets were solved using the FLUENT 6.1 Computational Fluid Dynamics (CFD) software package. The geometry and mesh were generated with the GAMBIT package. The velocity field of the air and the trajectories of drug droplets inside the funnel--the tube that delivers the drug from the nebulizer to the infant's mouth--and close to its exit are robust and do not show any appreciable differences among the three breathing phases studied. However, in other parts of the hood, air velocity, and particle motion largely depend on the infant's breathing and physiological state. The efficiency of drug delivery to the mouth during inspiration is found to be as high as 84%, whereas it is much smaller in the other two (common) breathing phases examined. Our results may be utilized to improve the hood design and to increase its efficacy for administration of aerosolized medications to infants.