The subject invention relates to viruses that are able to purge (reduce or eliminate) undesirable cells in a mixture of cells. Undesirable cells can include neoplastic cells, cells mediating graft-versus host diseases, and autoimmune cells. The subject invention also relates to the purging of undesirable cells from bone marrow or peripheral blood cell harvests in the treatment of mammals including cancer patients, transplant recipients, and patients with autoimmune disease.