Alex Best, 
Animal and Plant Sciences, Sheffield

Modelling the coevolution of parasites and their hosts

Understanding the dynamics of infectious diseases in human, animal and plant hosts 
is one of the biggest challenges for modern science, with considerable health, social 
and financial implications. Mathematical models of these host-parasite interactions 
can allow us to understand and predict the behaviour of many disease systems. Here I 
shall focus on the evolutionary dynamics of parasites and hosts, applying the evolutionary
framework of adaptive dynamics to a classic model of host-parasite interactions. I shall 
show how parasite infectivity and host defence may be expected to evolve, both in isolation
and when they coevolve with one another. Throughout I shall highlight the important role of
the evolutionary trade-offs on the eventual outcome, particularly focussing on the potential 
for variation to arise through evolutionary branching.