No, They keep asking the public for more information like they would know more than the guy they arrested.
There is no body so the police can come up with any scenario and this man, who knows he might be an addict or homeless. Police there usually go for "low hanging fruit", easy people they can pin it on cause they look the part no matter that there might not be a shred of real evidence. Cause she seemed to have some troubles when you read that eviction order. There was a man there with a knife and other stuff so to the police that is enough "evidence" especially when you can't give an alibi cause nobody knows when she disappeared. That is used against you then too. Juries hear that and they just convict. The idea that you actually need DNA & a body and some clear evidence without a doubt went the way of the Dodo long ago.