Following the introduction of the pertussis vaccine in the 1940s pertussis incidence decreased sharply in all industrialized countries until the 1980s, when unexpectedly large numbers of cases began to appear in teenagers and adults. Using an SIR model involving loss of immunity and immune-boosting upon reexposure, we review and attempt to explain three changes in patterns of pertussis infections since vaccination began. (1) The change in age distribution of infection, (2) the change from apparently stochastically driven 2-5 year cycles with peak cases in the summer, to deterministically driven 3-4 year cycles with both summer and winter peaks in the vaccine era, and (3) the overall increase in incidence despite consistently high vaccine coverage. We hypothesize that these patterns can be explained by a combination of significant levels of natural immune boosting in the pre-vaccine era, age-specific contact patterns, and a high proportion of subclinical secondary cases. To address these issues we analyze a set of nested models that incorporate all of the proposed mechanisms and we compare them to a detailed 19-year age-structured data set from Massachusetts. Age distributions are calculated analytically from probabilistic models and the dynamics and ages are generated using a suite of age-structured ODEs.
Results/Conclusions
We find that a model that incorporates only incidence-dependent immune-boosting can account for the increase in cases in older individuals, but does not allow for significantly higher incidence among teenagers than adults, as observed in the data. Inclusion of age-specific seasonality and contact rates allows for a better model fit to the observed data in this respect. The refined model also allows for the observed range of dynamical patterns, changing from point stability under low vaccine coverage to unstable limit cycles with a period in the 2-4 year range depending on parameter values. Interestingly, when the dynamical system is shifted into a different dynamical regime through enhanced vaccination and subsequent reduction in boosting, it significantly affects both the age distribution of cases and the total incidence.
