Epidemic amplification by correlated superspreading

Noah Silva de Leonardi; Benjamin D. Dalziel

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arXiv · 2509.15338

Epidemic amplification by correlated superspreading

Noah Silva de Leonardi·Benjamin D. Dalziel

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Abstract

Infectious pathogens often propagate by superspreading, which focusses onward transmission on disproportionately few infected individuals. At the same time, infector-infectee pairs tend to have more similar transmission potentials than expected by chance, as risk factors assort among individuals who frequently interact. A key problem for infectious disease epidemiology, and in the dynamics of complex systems, is to understand how structured variation in individual transmission will scale to impact epidemic dynamics. Here we introduce a framework that reveals how population structure shapes epidemic thresholds, through autocorrelation of individual reproductive numbers along chains of transmission. We show that chains of superspreading can sustain epidemics even when the average transmission rate in the host population is below one, and derive a mathematical threshold beyond which correlated superspreading allows epidemics in otherwise subcritical systems. Empirical analysis of 47 transmission trees for 13 human pathogens indicate self-organizing bursts of superspreading are common and that many trees are near the critical boundary. Vaccination campaigns that proceed up assortative hierarchies of transmission are predicted to sustain the force of infection until herd immunity is reached, providing a mechanistic basis for threshold dynamics observed in real-world settings. Conversely, modulating correlations in transmission, rather than mean or variance, could enable cities and other complex systems to develop immune-like capacities that suppress contagion while preserving core functions.

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Noah Silva de Leonardi, Benjamin D. Dalziel. 2025-09-18. Epidemic amplification by correlated superspreading. https://arxiv.org/abs/2509.15338

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