  We consider a chemo-repulsion model with quadratic production in a bounded
domain. Firstly, we obtain global in time weak solutions, and give a regularity
criterion (which is satisfied for $1D$ and $2D$ domains) to deduce uniqueness
and global regularity. After, we study two cell-conservative and
unconditionally energy-stable first-order time schemes: a (nonlinear and
positive) Backward Euler scheme and a linearized coupled version, proving
solvability, convergence towards weak solutions and error estimates. In
particular, the linear scheme does not preserve positivity and the uniqueness
of the nonlinear scheme is proved assuming small time step with respect to a
strong norm of the discrete solution. This hypothesis is reduced to small time
step in $nD$ domains ($n\le 2$) where global in time strong estimates are
proved. Finally, we show the behavior of the schemes through some numerical
simulations.
