Why are some diseases more virulent than others? Vector–borne diseases such as malaria and water–borne diseases such as cholera are generally more virulent than diseases spread by direct contagion. One factor that characterizes both vector– and water–borne diseases is their ability to spread over long distances, thus causing infection of susceptible individuals distant from the infected individual. Here we show that this ability of the pathogen to infect distant individuals in a spatially structured host population leads to the evolution of a more virulent pathogen. We use a lattice model in which reproduction is local but infection can vary between completely local to completely global. With completely global infection the evolutionarily stable strategy (ESS) is the same as in mean–field models while a lower virulence is predicted as infection becomes more local. There is characteristically a period of relatively moderate increase in virulence followed by a more rapid rise with increasing proportions of global infection as we move beyond a ‘critical connectivity’. In the light of recent work emphasizing the existence of ‘small world’ networks in human populations, our results suggests that if the world is getting ‘smaller’ (as populations become more connected) diseases may evolve higher virulence.