There are likely to be relatively few deaths from the human form of mad cow disease, vCJD, as a result of infected blood, scientists have suggested.
Measures have been put in place to prevent vCJD infection via transfusions
The London School of Hygiene and Tropical Medicine team says measures to protect the public have worked.
In a Royal Society journal, scientists predict just 50 deaths from this potential source of vCJD by 2080.
A UK expert said transfusions were the most likely way vCJD would be transferred in the future.
Researchers at the London School of Hygiene and Tropical Medicine used recent figures for blood donations and transfusions to provide data to base their predictions on.
They suggest there will be a total of around 60m transfusions by 2080.
So far, four people are known to have contracted vCJD (variant Creutzfeldt-Jakob Disease).
They were among a group of 66 who received blood transfusions from donors who went on to develop the disease.
A number of measures have been put in place to protect people who need transfusions from contracting vCJD.
These include withdrawing any blood products donated from a person who later develops the condition and ruling that no-one who has received a blood transfusion since 1980 can become a donor.
And, since 1998, white blood cells - which are the most likely to carry the infection - have been removed from blood used for transfusions.
However, in 2004, a study of 13,000 appendix and tonsil samples revealed that thousands of people may be unknowingly harbouring vCJD and raising concerns over the possible extent of vCJD transmission via blood transfusions.
The researchers said young people - those in their 20s, 30s and 40s - were most likely to donate blood, but that people aged 60 and over were most likely to need transfusions.
This, they say means it is possible for vCJD to be transferred from a young donor to an old recipient.
But, because of their age, these recipients would not go back to donate blood so even if someone was infected, the disease would not be passed back into the blood donor system.
This, along with the restrictions on who can donate blood brought in by the government, limits the number likely to die from vCJD contracted through blood transfusions.
Without those public health measures, the researchers say the worst case scenario puts the potential death toll over the same period at around 900.
Dr Azra Ghani, an epidemiologist who worked on the study, said: "Patients requiring blood transfusions do really need them, often because they are in a life-threatening situation, so we hope this study will reassure people of the remote risk of contracting this disease."
But she added: "One uncertainty is around the dangers linked to surgical instruments, because there you would not have the 'age protection' factor, and we know that contamination protection measures do not remove the risk.
"However there has been no evidence of a case of vCJD developing after exposure to contaminated instruments."
Professor Christopher Higgins, chair of the Spongiform Encephalopathy Advisory Committee (SEAC) which advises the government on diseases such as vCJD, said: "In the future, blood transfusions are going to be the most likely way of transmission.
"We have effectively eliminated the primary method, which was eating infected meat."
But he said the actual numbers at risk of contracting vCJD in this way could not be determined now because it was known some people could be infected but not show signs themselves.
"Until we know how many people are in this category we won't have reliable numbers as to how many people might get vCJD from transfusions."