Mixing in age-structured population models of infectious diseases
John Glasser1, Zhilan Feng, Andrew Moylan
1Centers for Disease Control and Prevention, Atlanta, GA 30333, USA. jglasser@cdc.gov
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.
Insights
Realistic modeling of infectious disease spread requires accurate representation of social mixing patterns. This study refines models to better capture preferential mixing between parents, children, and co-workers, improving transmission control strategies.
Area of Science:
- Epidemiology
- Mathematical Modeling
- Public Health
Background:
- Infectious disease control relies on understanding pathogen transmission dynamics.
- Accurate modeling of interpersonal contact patterns is crucial for evaluating control strategies.
- Traditional models often use proportionate or preferential mixing assumptions that may not fully capture real-world interactions.
Purpose of the Study:
- To refine mathematical models of infectious disease transmission by incorporating newly observed preferential mixing patterns.
- To develop updated formulas that account for age-specific contact fractions and non-uniform age distributions within groups.
- To provide a framework for estimating infection probabilities, rates, and reproduction numbers based on realistic contact data.
Main Methods:
- Refined existing formulas for social mixing matrices to include preferential contact patterns between specific groups (e.g., parents-children, co-workers).
- Estimated age-specific fractions of contacts and variances of Gaussian distributions to represent age differences more accurately.
- Applied the refined models to estimate transmission parameters for influenza and varicella using historical epidemiological data and contact surveys.
Main Results:
- The refined formulas successfully reproduce observed preferential mixing patterns in social contact data.
- Calculations demonstrated the ability to estimate infection probabilities, rates, and reproduction numbers for specific diseases.
- Age-related susceptibility patterns were observed, with generally declining susceptibility with age, but potential increases in certain age groups.
Conclusions:
- Updated mathematical models incorporating realistic social mixing patterns are essential for accurate infectious disease transmission assessment.
- The refined methodology provides a more robust tool for evaluating public health interventions aimed at controlling infectious diseases.
- Further research into age-specific contact patterns and susceptibility can enhance the precision of epidemiological models.
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