Learning about HIV's ecology from sequence data

I am going to give two examples of the use of HIV sequence data to learn about the within-host ecology of viral growth and clearance. In the first example we asked “how strong is the T cell immune response during an HIV infection?” We recast that question as: “how much longer does an infected cell live if it invisible to the T cell immune response?” We care about how strong different parts of the immune response are because of their role in vaccine-induced immunity. In the second example we ask “how does HIV persist in infected people whilst they are on drug therapy that is so good that virus can no longer be measured in their blood?” We care about this question because we can only hope to develop treatments that cure infection if the persistent pool of infection can be cleared. Expect lots of biology and a small number of equations.