Persona 4koma. Started off as a web manga before being picked up for serialization.

From MangaHelpers:
It's fairly obvious to Terui Chiaki that her classmate Ajikawa Yoshio has a crush on her. He is completely not boyfriend material in her eyes and, even if he was, Chiaki already has a boyfriend. Their mysterious teacher Mr. Yamada sees this relationship between the two students and offers an experiment. He is able to make copies of people and objects and does so with Chiaki, creating a copy of her, except the copy has no knowledge of her boyfriend. Yoshio will hit on the Chiaki copy, who is named Koaki, and he'll try to make her fall in love with him. After a specified amount of time, the copy and original will be combined back together and which ever love is stronger between the current boyfriend and Yoshio will overwrite all other emotions. So this love experiment begins and both Chiaki and Koaki, being the same person, thinks Yoshio has no chance in hell but with each passing day, some feelings begin to bubble.

Kenzaki Shin'ichi is leader of the Anti-Vector Task Squad. He's in charge of hunting down Vectors, humans that carry with them the deadly Resurrection Deficiency Syndrome, a disease that can keep someone from resurrecting when they die.