Sri Lanka struggled to contain the flow of runs in sunny conditions after lunch as Latham cruised to his 29th Test half-century
The world number 11 from England said on his Twitter feed on Wednesday that he had not yet fully recovered from the back problem he suffered during the Players Championship in Florida in May.
Rose was sidelined for a month before returning for the June 16-19 U.S. Open at Oakmont where he missed the cut.
"Following an intense summer schedule and discussion with my team, I have decided to take the next eight weeks off for rest and recovery," the 2013 U.S. Open champion said.
"As many of you know, during the Players Championship I experienced discomfort in my back from a disc herniation and was sidelined for the following month.
"I worked hard to be able to return at the U.S. Open but my ongoing tournament schedule, combined with heavy preparation for the Olympics, did not allow for full and proper recovery."
Like most of the leading players, Rose had a busy July-August schedule when two major championships and the Olympic golf in Rio de Janeiro were crammed into five weeks.
He also had to prepare for last week's Ryder Cup in Chaska, Minnesota where holders Europe were crushed 17-11 by the United States.
"At this point in my career it is important to invest in my body and this time off is crucial for me to return to peak performance," said Rose, 36.
"The remainder of the year has such a great run of tournaments and I am very disappointed to have to miss out on some of them."
Sri Lanka struggled to contain the flow of runs in sunny conditions after lunch as Latham cruised to his 29th Test half-century
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