The cheetah virus was a virus of the Cheetah People and their world, described as everything on the planet, the rocks and trees, having "an extra dimension." (PROSE: Survival) It contaminated other species and slowly turned them into new Cheetahs. It was a form of DNA corruption, related to the high amount of artron energy in the planet's magnetosphere that enabled the world to metamorphose living matter. (PROSE: First Frontier)
A great civilisation colonised the Cheetah World, but many succumbed to the virus and the survivors were wiped out by the Cheetah People. Once individuals became Cheetahs, they were part of the planet.
When the Master landed on the planet he caught the virus and gained control of the Kitlings, using them to teleport humans from Earth so he could use one of them to get off the planet, the virus transferring to a number of humans as well. When the Cheetah World was destroyed, the Seventh Doctor told Ace the survivors could still feel the planet inside them. While even Time Lord minds weren't strong enough to completely resist the virus, (TV: Survival) the Seventh Doctor theorised that the Master's corrupted Trakenite DNA was most affected. (PROSE: First Frontier)