My theory is it's their child who has gone back in time to prevent himself from being born. Can't think of anything else
I've had that theory as well, but isn't it only their mind that goes back in time, and not their body? So it wouldn't be possible for him to go back into a time where he doesn't exist.
But on the other hand, the author did put a good bit of effort into explaining how the disease works, with this secretion, so maybe that could have been used to make a time machine? But that's too far fetched imo.
But I am sure that Mirai is the primary target of the murderer. It's interesting as well that he seems to have a whole gang behind him, as there were multiple people beating the guy with the dreads to death, as well as the baseball bat guy