During treatment the HIV hides in blood cells called CD4 T-lymphocytes, which are responsible for the patient's immune response, by inserting its own genetic information into the DNA of the CD4 cells.
Researchers from the University of Liverpool measured the levels of integrated HIV in the CD4 cells of patients undergoing uninterrupted treatment for up to 14 years, comparing patients receiving treatment for different lengths of time.
The researchers discovered that the amount of HIV found to be integrated in the CD4 cells was undiminished from year 1 to year 14.
This process - a sort of silent HIV replication - means the virus does not need to copy itself, produce new virus particles, and infect new CD4 cells - but is automatically incorporated at the birth of the cell.
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Anti-retroviral therapy is given to HIV patients to stop the production of new virus which prevents the infection and death of CD4 T-lymphocytes and the further progression of the disease.
Advances in anti-retroviral therapy over the last 30 years mean that most patients can have their virus suppressed to almost undetectable levels and live a long and healthy life.
"This research shows that sadly, the HIV virus has found yet another way to escape our treatments," said Professor Anna Maria Geretti, who led the study.
"We always knew HIV is difficult to suppress completely and that it hides inside CD4 cells, but we always hoped that as the body gradually renews its CD4 cells then the hidden HIV would die out.
"We were surprised to find that the levels of HIV integrated in the CD4 cells didn't reduce over the 14-year period.
The research is published in the journal BioMedicine.