The First Rule of One Piece is “Never trust anything the World Government says”.
According to the World Government, Garp and Roger teamed up and defeated not only Rocks D. Xebec but the entire Rocks Pirates crew (which included Big Mom, Kaido, Edward Newgate and Shiki) causing them to disband after Rocks was killed.
But that doesn’t make sense even in One Piece. Even if Rocks is actually dead, none of the future Yonko were captured as they continued to thrive and prosper. Since they weren’t captured, it doesn’t seem that all of them were defeated at the raid by Garp and Roger at God Valley.
1) Rocks ate the Germ-Germ Fruit or a similar devil fruit which allowed him to infect people with a deadly virus.
2) Roger either fought Rocks as a youth and was infected, or Rocks attacked a young Roger and infected him. Thus, making Rocks Roger’s first and greatest enemy.
3) Whitebeard allied with Roger and Garp against Rocks.
4) Whitebeard was also infected either during or right before the God Valley incident.
The scene where both Roger and Whitebeard were sitting surrounded by Cherry Blossoms, talking for one last time, and the fact in One Piece Cherry Blossoms have healing and soothing properties, could hint that both men at the time were sick, possibly because of Rocks.
This would mean that Roger didn’t get sick four years before his death, like Rayleigh said, but was sick for a long time before, and four years prior to his death he got worse to the point of needing to bring Crocus on the ship as a doctor.
*Theory by Dettles