“After-birth abortion” is a term invented by two philosophers, Alberto Giubilini and Francesca Minerva. In the Journal of Medical Ethics, they propose:
[W]hen circumstances occur after birth such that they would have justified abortion, what we call after-birth abortion should be permissible. … [W]e propose to call this practice ‘after-birth abortion’, rather than ‘infanticide,’ to emphasize that the moral status of the individual killed is comparable with that of a fetus … rather than to that of a child. Therefore, we claim that killing a newborn could be ethically permissible in all the circumstances where abortion would be. Such circumstances include cases where the newborn has the potential to have an (at least) acceptable life, but the well-being of the family is at risk.