Epidemiological models with age structure, proportionate mixing, and cross-immunity

C. Castillo-Chavez, H. W. Hethcote, V. Andreasen, S. A. Levin, W. M. Liu

Research output: Contribution to journalArticlepeer-review

217 Scopus citations


Infection by one strain of influenza type A provides some protection (cross-immunity) against infection by a related strain. It is important to determine how this influences the observed co-circulation of comparatively minor variants of the H1N1 and H3N2 subtypes. To this end, we formulate discrete and continuous time models with two viral strains, cross-immunity, age structure, and infectious disease dynamics. Simulation and analysis of models with cross-immunity indicate that sustained oscillations cannot be maintained by age-specific infection activity level rates when the mortality rate is constant; but are possible if mortalities are age-specific, even if activity levels are independent of age. Sustained oscillations do not seem possible for a single-strain model, even in the presence of age-specific mortalities; and thus it is suggested that the interplay between cross-immunity and age-specific mortalities may underlie observed oscillations.

Original languageEnglish (US)
Pages (from-to)233-258
Number of pages26
JournalJournal of mathematical biology
Issue number3
StatePublished - May 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • Modeling and Simulation


  • Age structure
  • Cross-immunity
  • Infectious diseases
  • Influenza
  • Proportionate mixing


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