I will discuss mathematical models that describe the in vivo
dynamics of HIV infection. Two aspects will be examined: (a) the early
interactions between HIV and the immune system during acute infection. This
is a very important phase that determines the long term course of the
disease and that can be modulated by anti-viral drug therapy. (b) Possible
reasons for the transition from the disease-free phase of the infection to
the development of AIDS, and possible reasons for why naturally infected
monkeys can carry persistent high virus loads without ever developing AIDS.
This will be discussed in the context of viral evolution in vivo, and how
this is affected by the ability of multiple HIV particles to infect the same
cell, a recent experimental discovery.