Questions: Age-Structured Epidemiological Models

Question 1

For influenza, epidemiological models suggest vaccinating school-age children may reduce overall transmission more than vaccinating the elderly, even though elderly face higher mortality. Why?

• A. Children have stronger innate immunity and require fewer doses to achieve protection
• B. Children have higher contact rates and serve as transmission bridges to all other age groups
• C. The elderly are already protected by prior-season immunity, making vaccination redundant
• D. Vaccines are less immunogenic in elderly populations due to immunosenescence

Answer: (B)

Age-structured models reveal that optimal vaccination strategy depends on contact network structure, not just who faces the worst outcomes. School-age children have among the highest contact rates and act as hubs connecting family members and community groups. Vaccinating them reduces transmission broadly — an insight inaccessible to homogeneous-mixing models, which would recommend targeting whoever is most at risk of severe disease.

Question 2

In an age-structured epidemiological model, what does the dominant eigenvalue of the next-generation matrix represent?

• A. The average age at which primary infection occurs in a naive population
• B. The proportion of cases concentrated in the highest-contact age group
• C. R₀ for the age-structured system
• D. The peak per-capita transmission rate in the youngest age group

Answer: (C)

The next-generation matrix captures how many secondary infections each age group generates in each other group. Its dominant eigenvalue is the spectral radius, which equals R₀ for the structured system. The corresponding eigenvector gives the relative age distribution of cases at epidemic onset. This eigenvalue approach generalizes R₀ from homogeneous mixing to heterogeneous contact settings.

Question 3

In age-structured models, contact rates between age groups are typically assortative — people preferentially contact others of similar age — which means a diagonal-dominant WAIFW matrix is more realistic than a uniform one.

• T. True
• F. False

Answer: True

Empirical contact surveys like POLYMOD documented strong diagonal dominance in age-contact matrices: children contact mostly children, working adults contact other working adults, and so on. This assortative mixing means transmission introduced into one age group stays concentrated there initially, rather than spreading uniformly across all ages as homogeneous-mixing models assume.

Question 4

Homogeneous-mixing SIR models and age-structured SIR models will typically recommend the same optimal vaccination strategy, provided R₀ is equal in both models.

• T. True
• F. False

Answer: False

Equal R₀ does not imply equal transmission dynamics by age. For rubella, a homogeneous-mixing model would point vaccination toward the most-infected group (children), but age-structured models reveal that preventing congenital rubella syndrome requires protecting women of childbearing age — which demands vaccinating adults directly. Age-structured and homogeneous models diverge systematically when disease severity, contact rates, and susceptibility differ across age groups.

Question 5

Why does optimal vaccination strategy for rubella differ from what a homogeneous-mixing SIR model would predict, and what does this reveal about the model's limitation?

Model answer: Rubella's most severe outcomes (congenital rubella syndrome) occur when infection reaches pregnant women, not children. A homogeneous-mixing model targets the most-infected group, which is typically children, but age-structured models reveal that children's high contact rates do not translate into effective herd protection for pregnant women unless adult women are directly vaccinated. The limitation of homogeneous mixing is that it cannot represent differential exposure by age — it treats every person as equally likely to contact every other, which collapses the structural feature that makes age-targeted strategy matter.

This is the central practical payoff of age-structured modeling: it produces different — and more accurate — policy recommendations than homogeneous mixing whenever transmission patterns, clinical severity, and contact rates diverge by age. For rubella, measles, influenza, and COVID-19, the age-stratified recommendation differs from the homogeneous-mixing one in ways that change which populations are prioritized for vaccination.