Infection Dynamics on Small-World Networks

The use of network models to describe the impact of local spatial structure on the spread of infections is discussed. In particular, we focus on small-world networks, within which the pattern of interactions can be varied from being entirely local to being entirely global as a single parameter is changed. Analysis approaches from graph theory, statistical physics and mathematical epidemiology are discussed. Simulation results are presented that highlight the surprising findings of Watts and Strogatz [58], namely that a small number of long-range interactions in an otherwise locally structured population can markedly enhance the ability of an infection to spread and the rate at which the spread occurs. We also discuss some of the implications of such spatial structure on the dynamics and persistence of endemic infections.