  We present an updated version of the semi-analytic Just-Jahrei{\ss} (JJ)
model of the Galactic disk and constrain its parameters in the Solar
neighbourhood. The new features of the JJ model include a simple two-component
gaseous disk, a star-formation rate (SFR) function of the thick disk that has
been extended in time, and a correlation between the kinematics of molecular
gas and thin-disk populations. Here, we study the vertical number density
profiles and W-velocity distributions determined from ~2 million local stars of
the Gaia DR2. We also investigate an apparent Hess diagram of the Gaia stars
selected in a conic volume towards the Galactic poles. Using a stellar
evolution library, we synthesise stellar populations with a four-slope broken
power-law initial mass function (IMF), the SFR, and an age-metallicity relation
(AMR). The latter is consistently derived with the observed metallicity
distribution of the local Red Clump (RC) giants from the APOGEE. Working within
a Bayesian approach, we sample the posterior probability distribution in a
multidimensional parameter space using the MCMC method. We find that the
spatial distribution and motion of the Gaia stars imply two recent SF bursts
centered at ages of ~0.5 Gyr and ~3 Gyr and characterised by a ~30% and ~55% SF
enhancement, respectively, relative to a monotonously declining SFR continuum.
The stellar populations associated with this SF excess are found to be
dynamically hot for their age: they have W-velocity dispersions of ~12.5 km/s
and ~26 km/s. The new JJ model is able to reproduce the local star counts with
an accuracy of ~5 %. Using Gaia DR2 data, we self-consistently constrained 22
parameters of the updated JJ model. Our optimised model predicts two SF bursts
within the last ~4 Gyr, which may point to recent episodes of gas infall.
