  We present a theoretical investigation of the light, radius and radial
velocity variations of the prototype $\delta$ Cephei. We find that the best fit
model accounts for luminosity and velocity amplitudes with an accuracy better
than $0.8\sigma$, and for the radius amplitude with an accuracy of $1.7\sigma$.
The chemical composition of this model suggests a decrease in both helium (0.26
vs 0.28) and metal (0.01 vs 0.02) content in the solar neighborhood. Moreover,
distance determinations based on the fit of light curves agree at the
$0.8\sigma$ level with the trigonometric parallax measured by the Hubble Space
Telescope (HST). On the other hand, distance determinations based on angular
diameter variations, that are independent of interstellar extinction and of the
$p$-factor value, indicate an increase of the order of 5% in the HST parallax.
