In related proceedings pursuant to Family Court Act articles 6 and 10, the mother appeals (1), as limited by her brief, from stated portions of an order of disposition of the Family Court, Queens County (Salinitro, J.), dated December 18, 2012, made in proceeding No. 1, which, upon an order of fact-finding of the same court dated October 4, 2012, finding, inter alia, that she derivatively abused the child Amirah L., and after a dispositional hearing, among other things, limited the mother’s contact with Amirah L. to supervised visitation upon the release of the child to the custody of the biological father, (2) from an order of protection of the same court, also dated December 18, 2012, made in proceeding No. 1, which, inter alia, prohibited all unsupervised contact between her and Amirah L. up to and including December 18, 2013, and (3), as limited by her brief, from so much of a final order of custody of the same court, also dated December 18, 2012, made in proceeding No. 2, as, after a dispositional hearing, awarded her only supervised visitation with Amirah L. The appeal from the order of disposition brings up for review the order of fact-finding.
Ordered that the order of disposition and the final order of custody are affirmed insofar as appealed from, without costs or disbursements; and it is further,
Ordered that the appeal from the order of protection is dismissed as academic, without costs or disbursements.
The order of protection expired by its own terms on December 18, 2013, and the determination of the appeal from that order of protection would, under the facts of this case, have no direct effect on the parties (see Matter of Max F. [Emma F.-G.], 97 *796AD3d 816, 817 [2012]). Accordingly, we dismiss the appeal from the order of protection as academic.
Contrary to the mother’s contention, the Family Court’s finding that she derivatively abused the subject child, Amirah, was supported by a preponderance of the evidence adduced at the fact-finding hearing (see Family Ct Act § 1046 [b] [i]; cf. Matter of Amirah L. [Candice J.], 118 AD3d 792 [2014] [decided herewith]). The mother’s own medical expert opined that the injuries suffered by Amirah’s sister Anniyah were intentionally inflicted on three different occasions while she was in the mother’s care. Thus, the petitioner established a prima facie case of child abuse, and the burden shifted to the mother to rebut the evidence of her culpability (see Family Ct Act § 1046 [a] [ii]; Matter of Philip M., 82 NY2d 238, 244 [1993]; Matter of Robert A. [Kelly K.], 109 AD3d 611, 612-613 [2013]). As she concedes on appeal, the mother failed to provide a reasonable and adequate explanation for Anniyah’s injuries. Accordingly, the Family Court properly concluded that the mother abused Anniyah (see Matter of Robert A., 109 AD3d at 612-613; Matter of Nicholas S. [John T.], 107 AD3d 1307, 1310 [2013]). The nature of the abuse, which led to Anniyah’s death, and the circumstances in which it was committed, demonstrated that the mother’s judgment and understanding of her parental duties relating to the care of children were so defective as to create a substantial risk of harm to any child in her care. Accordingly, the Family Court properly found that the mother derivatively abused the subject child (see Family Ct Act §§ 1012 [e] [ii]; 1046 [a] [i]; Matter of Leah R. [Miguel R.], 104 AD3d 774, 774 [2013]).
The Family Court directed that the mother’s visitation with the subject child be supervised. Because the court’s determination that the visitation should be supervised has a sound and substantial basis in the record, we do not disturb it (see Matter of Hansen v Balkaran, 111 AD3d 827 [2013]; Matter of Roland Noele B., 66 AD3d 1008, 1009 [2009]).
Eng, EJ., Dillon, Balkin and Sgroi, JJ., concur.