  Despite high vaccine coverage, pertussis has re-emerged as a public health
concern in many countries. One hypothesis posed for re-emergence is the waning
of immunity. In some disease systems, the process of waning immunity can be
non-linear, involving a complex relationship between the duration of immunity
and subsequent boosting of immunity through asymptomatic re-exposure.
  We present and analyse a model of infectious disease transmission to examine
the interplay between infection and immunity. By allowing the duration of
infection-acquired immunity to differ from that of vaccine-acquired immunity,
we explore the impact of the difference in durations on long-term disease
patterns and prevalence of infection.
  Our model demonstrates that vaccination may induce cyclic behaviour, and its
ability to reduce the infection prevalence increases with both the duration of
infection-acquired immunity and duration of vaccine-acquired immunity. We find
that increasing vaccine coverage, while capable of leading to an increase in
overall transmission, always results in a reduction in prevalence of primary
infections, with epidemic cycles characterised by a longer interepidemic period
and taller peaks.
  Our results show that the epidemiological patterns of an infectious disease
may change considerably when the duration of vaccine-acquired immunity differs
from that of infection-acquired immunity. Our study highlights that for any
particular disease and associated vaccine, a detailed understanding of the
duration of protection and how that duration is influenced by infection
prevalence is important as we seek to optimise vaccination strategies.
