%0 Journal Article %1 Glasser20121 %A Glasser, J. %A Feng, Z. %A Moylan, A. %A Del Valle, S. %A Castillo-Chavez, C. %D 2012 %J Mathematical Biosciences %K Adult; Age Age-structured Child; Communicable Convex Cumulative Disease Diseases; Epidemiologic Face-to-face Factors; Gaussian Generation Humans; Incidence; Indirect Infection Infectious Intervention Kronecker Mathematical Methods; Mixing, Off-diagonal Outbreaks; Prevalence; Prospective Reproduction Studies Theoretical Young age article; assessment; children, combinations; comparison; computing; control; controlled conversation; delta; disease disease; distribution; effects; elements; factor, generation human; incidence; infection infection; infectious influenza; intermethod latent mathematical method; model; models, models; nonhuman; numbers; outcome pathogen, period; population probability; rate; rates; reliability; risk risk; sensitivity; size; structure; study; time; transmission; %N 1 %P 1-7 %R http://dx.doi.org/10.1016/j.mbs.2011.10.001 %T Mixing in age-structured population models of infectious diseases %U http://dx.doi.org/10.1016/j.mbs.2011.10.001 %V 235 %X 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. Â\copyright 2011.

@article{Glasser20121, abstract = {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. {\^A}{\copyright} 2011.}, added-at = {2017-11-10T22:48:29.000+0100}, affiliation = {Centers for Disease Control and Prevention, Atlanta, GA, United States; Purdue University, West Lafayette, IN, United States; Wolfram Research, Champaign, IL, United States; Los Alamos National Laboratory, Los Alamos, NM, United States; Arizona State University, Tempe, AZ, United States}, author = {Glasser, J. and Feng, Z. and Moylan, A. and Del Valle, S. and Castillo-Chavez, C.}, author_keywords = {Indirect effects; Interpersonal contacts; Intervention assessment; Preferential mixing; Transmission modeling}, biburl = {https://www.bibsonomy.org/bibtex/2bf897069ad5d0b822d81ab6011182071/ccchavez}, coden = {MABIA}, correspondence_address1 = {Glasser, J.1600 Clifton Road, NE, Mail Stop A-34, Atlanta, GA 30333, United States; email: jglasser@cdc.gov}, date-added = {2017-11-10 21:45:26 +0000}, date-modified = {2017-11-10 21:45:26 +0000}, document_type = {Article}, doi = {http://dx.doi.org/10.1016/j.mbs.2011.10.001}, interhash = {38098c7cf737de06e9e5193d8cc71942}, intrahash = {bf897069ad5d0b822d81ab6011182071}, issn = {00255564}, journal = {Mathematical Biosciences}, keywords = {Adult; Age Age-structured Child; Communicable Convex Cumulative Disease Diseases; Epidemiologic Face-to-face Factors; Gaussian Generation Humans; Incidence; Indirect Infection Infectious Intervention Kronecker Mathematical Methods; Mixing, Off-diagonal Outbreaks; Prevalence; Prospective Reproduction Studies Theoretical Young age article; assessment; children, combinations; comparison; computing; control; controlled conversation; delta; disease disease; distribution; effects; elements; factor, generation human; incidence; infection infection; infectious influenza; intermethod latent mathematical method; model; models, models; nonhuman; numbers; outcome pathogen, period; population probability; rate; rates; reliability; risk risk; sensitivity; size; structure; study; time; transmission;}, language = {English}, number = 1, pages = {1-7}, pubmed_id = {22037144}, timestamp = {2017-11-10T22:48:29.000+0100}, title = {Mixing in age-structured population models of infectious diseases}, url = {http://dx.doi.org/10.1016/j.mbs.2011.10.001}, volume = 235, year = 2012 }