  Consider the following stochastic model for immune response. Each pathogen
gives birth to a new pathogen at rate $\lambda$. When a new pathogen is born,
it has the same type as its parent with probability $1 - r$. With probability
$r$, a mutation occurs, and the new pathogen has a different type from all
previously observed pathogens. When a new type appears in the population, it
survives for an exponential amount of time with mean 1, independently of all
the other types. All pathogens of that type are killed simultaneously. Schinazi
and Schweinsberg (2006) have shown that this model on $\Z^d$ behaves rather
differently from its non-spatial version. In this paper, we show that this
model on a homogeneous tree captures features from both the non-spatial version
and the $\Z^d$ version. We also obtain comparison results between this model
and the basic contact process on general graphs.
