The Oxford teenager was last seen in the city on December 3 and did not return home that evening as planned.
"At this stage, we are keeping an open mind as to what has happened to Jayden," said Detective Chief Superintendent Andy Murray of Thames Vallley Police.
"Due to the length of time she has been missing and the fact that she has made no contact with her family or friends, we are treating her disappearance very seriously."
Officers arrested a 22-year-old man last night at an address in Reading on suspicion of murder. Forensic officers are examining the property.
Jayden is white, of slim build with shoulder-length dark brown hair and brown eyes.
She was wearing light blue faded jeans, a brown hooded top with red lettering on it, a black waist length jacket, and dark coloured trainers when she was last seen.
It is believed she walked up the High Street through the town centre, arriving at Oxford train station at 4.07pm, where she boarded a train to Didcot. The last sighting of her is when she left Didcot train station at about 4.27pm.
Officers are also in Upton, near Didcot.
Mr Murray said: "A number of lines of inquiries have led us to this area and we are asking residents whether they saw any suspicious activity on Sunday night into Monday morning.