Theory about the motives (spoiler)
In my opinion, there is enough evidence in the movie that proves we can change the past. Still, James's only mission is to find the original virus to help scientists develop a cure for the people in 2035. The question is, WHY? Why not try to stop the virus completely and save billions of people?
My theory is that scientists have become the ruling elite in 2035 "thanks" to the plague. They have become the government, making decisions and setting policies. Society has become dependent on this narrow layer of surviving scientists. A form of scientific dictatorship.
They don't want to give up their power, so they settle for saving themselves and the people who are still alive.