From The TimeSplitters Wiki

The Flame Games have been in both TS2 and TSFP. They both use flames for their main form of play.

Flame Tag

Flame Tag begins with one player on fire and it is passed on to another upon touching another person. The player with the least time holding the flame at the end of the game wins. This mode usually ends up with various winners, since it is very easy to avoid the person on fire. It did not appear in TSFP, most likely since it had so many glitches in the TS2 version.

Virus

Virus has appeared in both TS2 and TSFP. One player starts the round on fire (albeit a green flame) and the aim is to infect the other players on the map. A player cannot lose the virus, and will stay alight until the end of the match. The last person without the virus will win the match, and if the time elapses with two or more people untagged, they all win. Along with being caught, suicide will also result in being infected with the virus. In TSFP, players with the virus are given a slight boost of speed so that simply running in a straight line isn't enough to shake off any pursuers. It should be noted that if an infected player is killed, they will respawn, potentially blocking off an route of exit you may have hoped to take.