TY - JOUR
T1 - Mixing in age-structured population models of infectious diseases
AU - Glasser, John
AU - Feng, Zhilan
AU - Moylan, Andrew
AU - Del Valle, Sara
AU - Castillo-Chavez, Carlos
N1 - Funding Information:
We are grateful to Roger Germundsson for guiding J.G. during the 2009 Advanced Mathematica™ Summer School, Karl Hadeler for helpful discussions, two anonymous reviewers for constructive suggestions, and Nathaniel Hupert and Michael Washington for support. Recognizing the importance of mixing in population modeling, John Edmunds pioneered empirical studies of inter-personal contacts, several of which permitted this theoretical study and applications. Z.F.’s research is partially supported by IPA908630 between the CDC and Purdue University and NSF grant DMS-1022758 .
PY - 2012/1
Y1 - 2012/1
N2 - 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.
AB - 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.
KW - Indirect effects
KW - Interpersonal contacts
KW - Intervention assessment
KW - Preferential mixing
KW - Transmission modeling
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U2 - 10.1016/j.mbs.2011.10.001
DO - 10.1016/j.mbs.2011.10.001
M3 - Article
C2 - 22037144
AN - SCOPUS:84857999626
SN - 0025-5564
VL - 235
SP - 1
EP - 7
JO - Mathematical Biosciences
JF - Mathematical Biosciences
IS - 1
ER -