Trypanosoma brucei infects various domestic and wild mammals in equatorial
Africa. The parasite's genome contains several hundred alternative and high
ly diverged surface antigens, of which only a single one is expressed in an
y cell. Individual cells occasionally change expression of their surface an
tigen, allowing them to escape immune surveillance. These switches appear t
o occur in a partly random way, creating a diverse set of antigenic variant
s. In spite of this diversity, the parasitaemia develops as a series of out
breaks, each outbreak dominated by relatively few antigenic types. Host-spe
cific immunity eventually clears the dominant antigenic types and a new out
break follows from antigenic types that have apparently been present all al
ong at low frequency This pattern of sequential dominance by different anti
genic types remains unexplained. I use a mathematical model of parasitaemia
and host immunity to show that small variations in the rate at which each
type switches to other types can explain the observations. My model shows t
hat randomly chosen switch rates do not provide sufficiently ordered parasi
taemias to match the observations. Instead, minor modifications of switch r
ates by natural selection are required to develop a sequence of ordered par
asitaemias.