Experts have said it may be inevitable that new kinds of bird flu emerge that are "well-adapted to human beings".
Scientists have studied two men who caught the disease in China in December last year, as part of research published in medical journal The Lancet.
A 24-year-old man died, and it is thought he passed the disease on to his father, 52, who managed to survive with early medical intervention.
He was given anti-viral treatment and plasma cells from someone who had previously been vaccinated against bird flu.
It is believed the son caught the disease during a visit to a poultry market six days before he became ill.
In an accompanying comment Dr Jeremy Farrar and colleagues from Vietnam's Hospital for Tropical Diseases said: "Whatever the underlying determinants, if we continue to experience widespread, uncontrolled outbreaks of H5N1 in poultry, the appearance of strains well-adapted to human beings might just be matter of time.
"In the meantime, all family contacts of a patient with probable or confirmed H5N1 should be given chemoprophylaxis [drugs to prevent infection] and placed under surveillance.
"Personal protection and advice must be extended to the family members and health workers visiting and looking after patients in hospital."
Medics also tested 91 people who had come into contact with the infected men, but none of those had contracted H5N1.