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IRAS~04158+2805 has long been thought to be a very low mass T-Tauri star(VLMS) surrounded by a nearly edge-on, extremely large disc. Recentobservations revealed that this source hosts a binary surrounded by an extendedcircumbinary disc with a central dust cavity. In this paper, we combine ALMAmulti-wavelength observations of continuum and $^{12}$CO line emission, withH$\alpha$ imaging and Keck astrometric measures of the binary to develop acoherent dynamical model of this system. The system features an azimuthalasymmetry detected at the western edge of the cavity in Band~7 observations anda wiggling outflow. Dust emission in ALMA Band 4 from the proximity of theindividual stars suggests the presence of marginally resolved circumstellardiscs. We estimate the binary orbital parameters from the measured arc of theorbit from Keck and ALMA astrometry. We further constrain these estimates usingconsiderations from binary-disc interaction theory. We finally perform threeSPH gas + dust simulations based on the theoretical constraints; wepost-process the hydrodynamic output using radiative transfer Monte Carlomethods and directly compare the models with observations. Our results suggestthat a highly eccentric $e\sim 0.5\textrm{--}0.7$ equal mass binary, with asemi-major axis of $\sim 55$ au, and small/moderate orbital plane vs.circumbinary disc inclination $\theta\lesssim 30^\circ$ provides a good matchwith observations. A dust mass of $\sim 1.5\times 10^{-4} {\rm M_\odot}$ bestreproduces the flux in Band 7 continuum observations. Synthetic CO lineemission maps qualitatively capture both the emission from the central regionand the non-Keplerian nature of the gas motion in the binary proximity.

Circumbinary and circumstellar discs around the eccentric binary IRAS 04158+2805 -- a testbed for binary-disc interaction