Background/Question/Methods
Deterministic SIR-type models of pertussis (whooping cough) dynamics do not fully explain the observed periodicity and variability of pertussis dynamics globally, or the recent resurgence of pertussis in the presence of high vaccine coverage.  There is empirical and theoretical evidence for variable pertussis dynamics, even in times and places with similar birth rates, vaccine coverage, and other key demographic features.  We previously fit a model that incorporated waning and boosting of immunity to age-specific pertussis incidence data from both pre- and post-vaccine era settings.  Cyclic and fixed point attractors coexisted for the estimated parameter values in the absence of seasonal forcing or vaccination.  Here, we explore the hypothesis that this model can help to explain the variability in pertussis dynamics globally, as well as the apparent variability within a single time series.  We use statistical techniques to reconstruct the most likely time series of susceptible individuals using data on births, infections, and waning of immunity.  We compare differences between the Susceptible-Infected phase plane of the two putative dynamical regimes in the data, with the dynamics predicted by the model at each attractor.  We also quantify the amount of stochasticity needed to shift from one dynamical regime to the other.

Results/Conclusions
We find the time series can exhibit two different dynamical regimes: (1) Small amplitude cycles with a slightly variable period and high noise to signal ratio, and (2) large amplitude cycles with a consistent three year period and a low noise to signal ratio.  We find that the deterministic form of our model allows for more variable dynamics than previous pertussis models, particularly in the absence of vaccination.  When seasonality is incorporated, a small perturbation away from the large amplitude cyclic attractor (driven primarily by immune waning and boosting) returns to the attractor much more quickly than a perturbation from the small amplitude cycles (driven by the interaction of seasonality and damped oscillations), suggesting that noise is more quickly damped out in the large amplitude regime than the small, as observed in the data.  Additionally, preliminary analyses of the basins of attraction in the model and the susceptible reconstruction from data suggest that, in the presence of mild stochasticity, switching between dynamical regimes is plausible in low birth rate countries during the prevaccine era.