Modelling the Evolution and Spread of HIV Immune Escape Mutants

During infection with human immunodeficiency virus (HIV), immune pressure from cytotoxic T-lymphocytes (CTLs) selects for viral mutants that confer escape from CTL recognition. These escape variants can be transmitted between individuals where, depending upon their cost to viral fitness and the CTL responses made by the recipient, they may revert. The rates of within-host evolution and their concordant impact upon the rate of spread of escape mutants at the population level are uncertain. Here we present a mathematical model of within-host evolution of escape mutants, transmission of these variants between hosts and subsequent reversion in new hosts. The model is an extension of the well-known SI model of disease transmission and includes three further parameters that describe host immunogenetic heterogeneity and rates of within host viral evolution. We use the model to explain why some escape mutants appear to have stable prevalence whilst others are spreading through the population. Further, we use it to compare diverse datasets on CTL escape, highlighting where different sources agree or disagree on within-host evolutionary rates. The several dozen CTL epitopes we survey from HIV-1 gag, RT and nef reveal a relatively sedate rate of evolution with average rates of escape measured in years and reversion in decades. For many epitopes in HIV, occasional rapid within-host evolution is not reflected in fast evolution at the population level.Author Summary: HIV evolves so quickly that it can be seen to adapt within one infected person. Evolutionary escape from immunity is particularly well-described. Escape variants transmit to new hosts, where they may revert. We present a mathematical model of three processes: within-host evolution of escape mutants, transmission of those variants between hosts and subsequent reversion in new hosts. Using this model we reconcile diverse datasets on HIV immune escape, highlighting where multiple data sources agree or disagree on the underlying rate processes. The several-dozen immune epitopes we survey reveal a relatively sedate rate of evolution with average rates of escape measured in years and reversion in decades. Although there are frequent reports in the literature of early and rapid within-host evolution of HIV, for many epitopes this is not reflected in fast evolution at the population level.