A reward of £8,000 has been offered by a family desperate for information or the whereabouts of a missing relative.
Former teacher Margaret Elliott, 75, of Barnford Crescent, Oldbury, who has advanced Alzheimer's has not been seen since 28 June.
More than 200 people joined a search in Oldbury for her last weekend.
Her daughter Kate Elliott said she would be extremely disorientated and confused by now. Police said they were "gravely concerned".
Det Insp Gary Dring said she could be anywhere.
"She may have got on a bus or maybe a train and travelled unwittingly to another part of the country," he said.
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