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

Towards a fully consistent Milky Way disk model -- IV. The impact of Gaia DR2 and APOGEE