As vaccination levels increase and a disease progresses towards elimination within a subpopulation it goes through several dynamical regimes. The first, when vaccination pressure is relatively low and the disease is endemic, is often characterized by regular epidemic cycles within the population. These have been well described, across many diseases in many locations. At high levels of vaccination, the endemic state is disease-free and reintroduction will result in short chains of transmission leading to rapid extinction. However, at intermediate vaccination pressure, occasional introduction events will spark outbreaks that may be off-cycle with endemic outbreaks. This regime may be characterized by the waiting time between outbreaks, or duration of epidemic fade-out. However, in the real world, data collection rarely happens at the subpopulation level - administrative units often comprise multiple epidemiological subpopulations. At the aggregate, or metapopulation, scale, epidemic fade-out may be rare and thus a poor indicator of progression to elimination. We use both simulations of SIR dynamics in an epidemic metapopulation and 30 years of measles surveillance at the county level from six provinces in China to evaluate patch- and metapopulation-level indicators of the transition to elimination.
Results/Conclusions
As a metapopulation progresses towards elimination, the time series dynamics change considerably. Our models suggest that as a metapopulation proceeds towards elimination, the variance of the phase of each annual epidemic will increase. That is, when outbreaks are mostly driven by endemic transmission, patch-level outbreaks will be synchronous. When patch-level fade-out between outbreaks becomes relatively common and many outbreaks are sparked by reintroduction events instead of endemic transmission, the timing when epidemic peaks occur each year becomes much more varied. This variance increases before vaccination in each subpopulation reaches the critical level required for elimination, and does not saturate until well after vaccination in each subpopulation reaches that critical level. Plotted in radial coordinates, we can characterize this variance using a scale-free measure that we propose as an indicator of transition to the patch-level and metapopulation-level elimination threshold. We quantify the progression in this measure of cycle variance using county-level (e.g. patch) and province-level (e.g. metapopulation) measles case data from a 30-year time series for six provinces in China and compare to recorded vaccination coverage to validate this pattern.