  In the current paper, we further develop the model for the migration of
planets introduced in Del Popolo et al. (2001) and extended to time-dependent
accretion discs in Del Popolo and Eksi (2002). We use a method developed by
Stepinski and Valageas (1996, 1997), that is able to simultaneously follow the
evolution of gas and solid particles for up to $10^7 {\rm yr}$. The disc model
is coupled to the migration model introduced in Del Popolo et al. (2001) in
order to obtain the migration rate of the planet in the planetesimal disc. We
find that in the case of discs having total mass of $10^{-3}-0.1 M_{\odot}$,
and $0.1<\alpha<0.0001$, planets can migrate inward a large distance while if
$M<10^{-3} M_{\odot}$ the planets remain almost in their initial position for
$0.1<\alpha<0.01$ and only in the case $\alpha<0.001$ the planets move to a
minimum value of orbital radius of $\simeq 2 {\rm AU}$. The model gives a good
description of the observed distribution of planets in the period range 0-20
days.
