Data from: Age-structure and transient dynamics in epidemiological systems

Mathematical models of childhood diseases date back to the early twentieth
century. In several cases, models that make the simplifying assumption of
homogeneous time-dependent transmission rates give good agreement with
data in the absence of secular trends in population demography or
transmission. The prime example is afforded by the dynamics of measles in
industrialized countries in the pre-vaccine era. Accurate description of
the transient dynamics following the introduction of routine vaccination
has proved more challenging, however. This is true even in the case of
measles which has a well-understood natural history and an effective
vaccine that confers long-lasting protection against infection. Here, to
shed light on the causes of this problem, we demonstrate that, while the
dynamics of homogeneous and age-structured models can be qualitatively
similar in the absence of vaccination, they diverge subsequent to vaccine
roll-out. In particular, we show that immunization induces changes in
transmission rates, which in turn reshapes the age distribution of
infection prevalence, which effectively modulates the amplitude of
seasonality in such systems. To examine this phenomenon empirically, we
fit transmission models to measles notification data from London that span
the introduction of the vaccine. We find that a simple age-structured
model provides a much better fit to the data than does a homogeneous
model, especially in the transition period from the pre-vaccine to the
vaccine era. Thus, we propose that age structure and heterogeneities in
contact rates are critical features needed to accurately capture transient
dynamics in the presence of secular trends.