Mixing in age-structured population models of infectious diseases

John Glasser, Zhilan Feng, Andrew Moylan, Sara Del Valle, Carlos Castillo-Chavez

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


Infectious diseases are controlled by reducing pathogen replication within or transmission between hosts. Models can reliably evaluate alternative strategies for curtailing transmission, but only if interpersonal mixing is represented realistically. Compartmental modelers commonly use convex combinations of contacts within and among groups of similarly aged individuals, respectively termed preferential and proportionate mixing. Recently published face-to-face conversation and time-use studies suggest that parents and children and co-workers also mix preferentially. As indirect effects arise from the off-diagonal elements of mixing matrices, these observations are exceedingly important. Accordingly, we refined the formula published by Jacquez et al. [19] to account for these newly-observed patterns and estimated age-specific fractions of contacts with each preferred group. As the ages of contemporaries need not be identical nor those of parents and children to differ by exactly the generation time, we also estimated the variances of the Gaussian distributions with which we replaced the Kronecker delta commonly used in theoretical studies. Our formulae reproduce observed patterns and can be used, given contacts, to estimate probabilities of infection on contact, infection rates, and reproduction numbers. As examples, we illustrate these calculations for influenza based on " attack rates" from a prospective household study during the 1957 pandemic and for varicella based on cumulative incidence estimated from a cross-sectional serological survey conducted from 1988-94, together with contact rates from the several face-to-face conversation and time-use studies. Susceptibility to infection on contact generally declines with age, but may be elevated among adolescents and adults with young children.

Original languageEnglish (US)
Pages (from-to)1-7
Number of pages7
JournalMathematical Biosciences
Issue number1
StatePublished - Jan 2012


  • Indirect effects
  • Interpersonal contacts
  • Intervention assessment
  • Preferential mixing
  • Transmission modeling

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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