B767 FLT CREW HAS ILL PAX WHILE AT CRUISE. DECLARES EMER AND DIVERTS.

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PAX SEATED IN THE AFT CABIN WAS VERY ILL. PAX 79 YRS OLD WAS FOUND VOMITING IN HER SLEEP; INCOHERENT TO HER SURROUNDINGS. THE FLT ATTENDANTS WERE IN THE PROCESS OF REVIVING PAX AND HAD ALERTED FO ABOUT 70 MINS N OF ZZZ. FO COMMANDED THE RELIEF PLT TO FLY THE AIRPLANE AND FLT ATTENDANTS TO AWAKEN AND NOTIFY ME OF OUR STATUS. WHEN I RPTED TO THE FLT DECK; FO WAS IN THE PROCESS OF PAGING THE CABIN FOR A PHYSICIAN ON BOARD WITH DISPATCH AND PHYSICIAN ON CALL ON A 3-WAY CALL OVER SATCOM. AT THIS TIME A PHYSICIAN ON BOARD CAME FORWARD AS NOTED BY FLT ATTENDANTS. RPTS AT THIS TIME FROM THE FLT ATTENDANTS WERE THAT THE PHYSICIAN ON BOARD WAS EXPERIENCING DIFFICULTY REVIVING PAX. THE PHYSICIAN ON BOARD CONFIRMED THAT PAX WOULD MOST LIKELY CONTINUE TO VOMIT DUE TO SOME GASTRO INTESTINAL DISORDER THAT A TRAVELING COMPANION OF PAX CONFIRMED SHE WAS TAKING SOME TYPE OF MEDICATION FOR. WE WERE ALSO CONCERNED WITH THIS ADDITIONAL INFO THAT PAX WOULD BECOME RAPIDLY DEHYDRATED. AT THIS POINT WE NOTIFIED DISPATCH OF OUR STATUS AND JOINTLY CONCLUDED WE WOULD DECLARE A MEDICAL EMER AND DIVERT. DECLARED A MEDICAL EMER WITH CTL. REVIEWED OVERWT LNDG CRITERIA AND PROCS. BRIEFED OUR ARR AND APCH. LNDG FLAPS 25 DEGS TO A SMOOTH LNDG 3900 LBS OVERWT. MEDICAL PERSONNEL BOARDED THE ACFT AND ASSISTED IN THE DEPLANING OF PAX.