  We report the effect of including repulsive interactions on various
thermodynamic observables calculated using a S-matrix based Hadron Resonance
Gas (HRG) model to already available corresponding results with only attractive
interactions [A. Dash, S. Samanta, and B. Mohanty, Phys. Rev. C 97, 055208
(2018)]. The attractive part of the interaction is calculated by parameterizing
the two body phase shifts using K-matrix formalism while the repulsive part is
included by fitting to the experimental phase shifts which carry the
information about the nature of the interaction. We find that the bulk
thermodynamic variables for a gas of hadrons such as energy density, pressure,
entropy density, speed of sound and specific heat are suppressed by the
inclusion of repulsive interactions and are more pronounced for second and
higher order correlations and fluctuations, particularly for the observables
$\chi^2_Q$, $\chi^2_B-\chi^4_B$ and $C_{BS}$ in the present model. We find a
good agreement between lattice QCD simulations and the present model for
$C_{BS}$. We have also computed two leading order Fourier coefficients of the
imaginary part of the first order baryonic susceptibility at imaginary baryon
chemical potential within this model and compared them with the corresponding
results from lattice. Additionally, assuming that the value of interacting
pressure versus temperature for a gas of hadrons calculated in S-matrix
formalism is same as that from a van der Waals HRG (VDWHRG) model, we have
quantified the attractive and repulsive interactions in our model in terms of
attractive and repulsive parameters used in the VDWHRG model. The values of
parameters thus obtained are $a=1.54\pm 0.064$ GeV $\text{fm}^{3}$ and
$r=0.81\pm 0.014$ fm.
