Modelling the long-term dynamics of pre-vaccination pertussis

Ganna Rozhnova, Ana Nunes

Research output: Contribution to journalArticleAcademicpeer-review


The dynamics of strongly immunizing childhood infections is still not well understood. Although reports of successful modelling of several data records can be found in the previous literature, the key determinants of the observed temporal patterns have not yet been clearly identified. In particular, different models of immunity waning and degree of protection applied to disease- and vaccine-induced immunity have been debated in the previous literature on pertussis. Here, we study the effect of disease-acquired immunity on the long-term patterns of pertussis prevalence. We compare five minimal models, all of which are stochastic, seasonally forced, well-mixed models of infection, based on susceptible-infective-recovered dynamics in a closed population. These models reflect different assumptions about the immune response of naive hosts, namely total permanent immunity, immunity waning, immunity waning together with immunity boosting, reinfection of recovered and repeat infection after partial immunity waning. The power spectra of the output prevalence time series characterize the long-term dynamics of the models. For epidemiological parameters consistent with published data, the power spectra show quantitative and even qualitative differences, which can be used to test their assumptions by comparison with ensembles of several-decades-long pre-vaccination data records. We illustrate this strategy on two publicly available historical datasets.

Original languageEnglish
Pages (from-to)2959-70
Number of pages12
JournalJournal of the Royal Society Interface
Issue number76
Publication statusPublished - 7 Nov 2012


  • Child
  • Computer Simulation
  • Disease Outbreaks/prevention & control
  • Humans
  • Models, Immunological
  • Prevalence
  • Seasons
  • Stochastic Processes
  • Whooping Cough/epidemiology


Dive into the research topics of 'Modelling the long-term dynamics of pre-vaccination pertussis'. Together they form a unique fingerprint.

Cite this