Aims.We present an updated version of the semi-analytic Just-Jahrei (JJ) model of the Galactic disk and constrain its parameters in the Solar neighbourhood.Methods.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 andW-velocity distributions determined from ∼2 × 106local stars of the secondGaiadata release (DR2). We also investigate an apparent Hess diagram of theGaiaDR2 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, the SFR, and an age-metallicity relation. The latter is consistently derived with the observed metallicity distribution of the local Red Clump giants from the Apache Point Observatory Galactic Evolution Experiment (APOGEE). Working within a Bayesian approach, we sample the posterior probability distribution in a multidimensional parameter space using the Markov chain Monte Carlo method.Results.We find that the spatial distribution and motion of theGaiaDR2 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 haveW-velocity dispersions of ∼12.5 km s−1and ∼26 km s−1. The new JJ model is able to reproduce the local star counts with an accuracy of ∼5%.Conclusions.UsingGaiaDR2 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.