  The present work deals with the study of spherical collapse of matter density
contrast in a latetime cosmological model with a reconstructed effective
equation of state. The linear and nonlinear evolution of matter density
contrast are studied. The variation of the critical density at collapse of the
spherical overdense region along redshift are also investigate. Further the
number count of collapsed object or the dark matter halos, equivalent to the
number count of galaxy clusters, are also studied. Two different halo mass
function formulations, namely the Press-Schechter mass function and the
Sheth-Tormen mass function, are adopetd to study the cluster number count along
the redshift. Similar analysis is also carried out for wCDM dark energy model
to have a direct comparison with the reconstructed effective equation of state
model. These two models are highly degenerate at the background and linear
level of matter perturbation. But the nonlinear evolution of matter overdensity
breaks the degeneracy. The reconstructed effective equation of state model
shows a substantial suppression in the cluster number count compared to wCDM
for redshift z > 0.5, and for z < 0.5, the number count is slightly higher than
that of wCDM.
