  Cytotoxic T lymphocytes (CTLs) are immune system cells that are thought to
play an important role in controlling HIV infection. We develop a stochastic
ODE model of HIV-CTL interaction that extends current deterministic ODE models.
Based on this stochastic model, we consider the effect of CTL attack on
intrahost HIV lineages assuming CTLs attack several epitopes with equal
strength. In this setting, we introduce a limiting version of our stochastic
ODE under which we show that the coalescence of HIV lineages can be described
by a simple paintbox construction. Through numerical experiments, we show that
our results under the limiting stochastic ODE accurately reflect HIV lineages
under CTL attack when the HIV population size is on the low end of its
hypothesized range. Current techniques of HIV lineage construction depend on
the Kingman coalescent. Our results give an explicit connection between CTL
attack and HIV lineages.
