Dependence Structure and Epidemic Outcomes in Heterogeneous SIR Models

Fuente: arXiv
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Autor principal: Khalifi, Mohamed El
Formato: Preprint
Publicado: 2026
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author Khalifi, Mohamed El
author_facet Khalifi, Mohamed El
contents We study a well mixed SIR epidemic model with heterogeneous susceptibility and infectivity, allowing for an arbitrary joint distribution of these traits. Using an exact final size formulation and a branching process approximation for early epidemic dynamics, we show that both the final epidemic size and the probability of a major outbreak are monotone with respect to the concordance order of the joint susceptibility infectivity distribution. In particular, among all couplings with fixed marginal trait distributions, comonotonic dependence maximizes epidemic severity, yielding sharp distribution free upper bounds. A key implication is that epidemic outcomes cannot be ordered by susceptibility heterogeneity alone: while increasing susceptibility variance reduces the final size under independence, positive dependence between susceptibility and infectivity can locally increase epidemic size for any basic reproduction number exceeding one. We further show that neither susceptibility variance nor the sign of the covariance suffices to determine epidemic severity under dependence. These findings offer new insights into epidemic risk assessment under limited information.
format Preprint
id arxiv_https___arxiv_org_abs_2601_01549
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Dependence Structure and Epidemic Outcomes in Heterogeneous SIR Models
Khalifi, Mohamed El
Populations and Evolution
We study a well mixed SIR epidemic model with heterogeneous susceptibility and infectivity, allowing for an arbitrary joint distribution of these traits. Using an exact final size formulation and a branching process approximation for early epidemic dynamics, we show that both the final epidemic size and the probability of a major outbreak are monotone with respect to the concordance order of the joint susceptibility infectivity distribution. In particular, among all couplings with fixed marginal trait distributions, comonotonic dependence maximizes epidemic severity, yielding sharp distribution free upper bounds. A key implication is that epidemic outcomes cannot be ordered by susceptibility heterogeneity alone: while increasing susceptibility variance reduces the final size under independence, positive dependence between susceptibility and infectivity can locally increase epidemic size for any basic reproduction number exceeding one. We further show that neither susceptibility variance nor the sign of the covariance suffices to determine epidemic severity under dependence. These findings offer new insights into epidemic risk assessment under limited information.
title Dependence Structure and Epidemic Outcomes in Heterogeneous SIR Models
topic Populations and Evolution
url https://arxiv.org/abs/2601.01549