  During an infection, HIV experiences strong selection by immune system T
cells. Recent experimental work has shown that MHC escape mutations form an
important pathway for HIV to avoid such selection. In this paper, we study a
model of MHC escape mutation. The model is a predator-prey model with two prey,
composed of two HIV variants, and one predator, the immune system CD8 cells. We
assume that one HIV variant is visible to CD8 cells and one is not. The model
takes the form of a system of stochastic differential equations. Motivated by
well-known results concerning the short life-cycle of HIV intrahost, we assume
that HIV population dynamics occur on a faster time scale then CD8 population
dynamics. This separation of time scales allows us to analyze our model using
an asymptotic approach.
  Using this model we study the impact of an MHC escape mutation on the
population dynamics and genetic evolution of the intrahost HIV population. From
the perspective of population dynamics, we show that the competition between
the visible and invisible HIV variants can reach steady states in which either
a single variant exists or in which coexistence occurs depending on the
parameter regime. We show that in some parameter regimes the end state of the
system is stochastic. From a genetics perspective, we study the impact of the
population dynamics on the lineages of HIV samples taken after an escape
mutation occurs. We show that the lineages go through severe bottlenecks and
that the lineage distribution can be characterized by a Kingman coalescent.
