Measurements of NmF2 and hmF2 at Millstone Hill are compared with results from the Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation (IZMIRAN) time-dependent mathematical model of the Earth's ionosphere and plasmasphere during the periods March 16--23 and April 6--12, 1990. The effects of vibrationally excited N2 are studied by using two approaches: (1) obtaining a full solution of the vibrational quanta continuity equation and (2) calculating an analytical solution of the steady state vibrational quanta continuity equation using a simple FORTRAN subroutine. It is shown that during both undisturbed periods and magnetic storms the full solution and the analytical approach give very similar results for NmF2 and hmF2 derived from the IZMIRAN model, so the analytical approach can be recommended for use in ionospheric models for calculation of electron densities during both quiet and disturbed conditions. ¿ American Geophysical Union 1996