Regular fluctuations in the incidence of immunizing infections exemplify the emergence of stable patterns in complex populations. Stable annual or biennial cycles in disease incidence occur in a variety of host-pathogen systems because of a common demographic clockwork, consisting of depletion of the susceptible population by infection or vaccination followed by recruitment through birth or waning immunity, modulated by seasonal fluctuations in transmission rates. High amplitude fluctuations in transmission rates can cause nonlinear dissonances in the demographic clock, leading to unpredictable variation in epidemic sizes that show sensitive dependence on initial conditions?deterministic chaos. However, this is hypothesized to be rare, because sufficiently large oscillations in transmission rates are uncommon, and would result in deep epidemic troughs that predispose the system to stochastic extinction. I will discuss recent work with collaborators analyzing epidemic data that describe a ubiquitous path to locally persistent deterministic chaos through small shifts in the seasonal pattern of transmission, rather than through high amplitude fluctuations in transmission rates. We base our analysis on a comparison of measles incidence in 80 major cities in the prevaccination era US and UK. Unlike the regular limit cycles of the UK series, the US data exhibit spontaneous shifts in epidemic periodicity, due to a slight lengthening of the seasonal period of low transmission associated with school summer holidays. These local dynamics resulted in spatially decorrelated epidemics across the US during the early 20th century. This shows that subtle systematic changes in host behavior can fundamentally alter the spatiotemporal coherence of epidemics, without significantly impacting pathogen persistence, globally or locally. Routes to deterministic chaos in population dynamics may therefore be prevalent.