(Covers information from Anderson's universe)
James Marcus "discovered" the T-virus in his attempt to save his daughter, Alicia, from an early death from Progeria. With the virus successful, his parnership with Isaacs in creating Umbrella led to the virus being used as a treatment for other conditions. However, it was discovered too late that the virus was capable of reanimating the bodies of people using the treatment and turning them into violent cannibalistic people later called the "Undead". The incident was covered up by Isaacs.
Concerned of more transfomations, Marcus called for research and development to be shut down. Isaacs, considering its application as a weapon, had Marcus murdered by Albert Wesker to prevent this.
Marcus is credited with the creation of the T-virus in Resident Evil: The Final Chapter, though Dr. Charles Ashford received that credit in Resident Evil: Apocalypse. While it is possible the two worked together in research, it is also possible this is a retcon.