Shinjuku DxD

Kabukicho, Shinjuku—the district that burns with desire is struck by an incurable disease. In this district, a doctor, Inui Date, runs a small medical clinic. Night after night, patients with extraordinary cases come to the clinic, when one day, a troublesome patient, detective Maria Daigo, appears. Set in a Shinjuku that has been plagued by an incurable disease, the doctor and the detective become entangled in one mysterious case after another as they face the darkness in this psychological thriller. Will the two be able to save this town?

(Source: MangaBox)

Note: Manga ends at chapter 41, however Volumes 1-3 each contain an omake chapter, bringing the total to 44 chapters.