A theoretical study of the role of spatial population structure in the evolution of parasite virulence.

*(English)*Zbl 1275.92083Summary: The rich theory of infectious disease modelling using the susceptible-infectious-recovered (SIR) framework is mainly based on the assumption of a well-mixed population, under which evolutionary behaviours (typically derived using adaptive dynamics) are shown to depend critically on the qualitative features of a virulence-transmission trade-off. Spatial extensions of this work, using simulation studies, show multiple evolutionary outcomes, which strongly depend on trade-off shape and, additionally, the length scale of the infectious process. In this paper, we aim to shed analytical insight into the mechanisms underlying these spatial evolutionary outcomes. In particular, why there is a qualitative difference observed in the evolutionary predicted virulence rates between linear and decelerating trade-offs between transmission and virulence and how recovery can weaken the effect of space. We use both pair approximations and cellular automata to model the spatial populations and the analysis exploits small neighbourhood variations in the spatial settings. The evolutionary outcomes are derived using adaptive dynamics.