COS 132-3 - Re-examining pertussis cycles and the role of waning immunity

Friday, August 12, 2011: 8:40 AM
10B, Austin Convention Center
Jennie S. Lavine, Biology, The Pennsylvania State University, University Park, PA, Aaron King, Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI and Ottar N. Bjornstad, Entomology, Penn State University, University Park, PA

Large infectious disease outbreaks are of both theoretical interest and public health concern.  Despite high vaccine coverage, epidemics of pertussis (whooping cough) have re-emerged throughout much of the developed world.  The re-emergence was unexpected and has led researchers to reconsider previously accepted ideas of the duration of immunity and the cause of large, cyclic outbreaks.  Early models of pertussis dynamics explained the observed patterns of incidence through a combination of lifelong immunity, seasonality and stochasticity.  However, in the past few decades, clinical and epidemiological evidence has mounted for rapidly waning immunity.  We propose to reconcile these issues by allowing for a very rapid anamenestic response, that is, rapid immune boosting upon secondary exposure.  We analyze a discrete time model that incorporates immune waning and boosting and fit the model to data from the prevaccine era in Copenhagen using an iterated filtering algorithm to make inference regarding the importance of waning and boosting in the cyclic dynamics of pertussis.


The data on pertussis incidence from Copenhagen in the early 20th century show a pattern of mixed dynamics, with multi-annual cycles sometimes dominated by low-amplitude, high-noise fluctuations, and other times exhibiting large outbreaks at regular intervals.  Our model with both waning and boosting of immunity exhibits a wide variety of dynamical behavior and predicts cyclic dynamics even in the absence of stochasticity and seasonality.  Interestingly, for a plausible range of parameter space, these cycles coexist with a stable fixed point attractor, allowing for the possibility of switching between deterministically and stochastically driven epidemics, as seen in the data.  The qualitative results thus far support the hypothesis that waning and boosting immunity drove the large pertussis outbreaks in prevaccine-era Copenhagen, however the final test will lie in the specific parameter estimates we obtain using iterated filtering.

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