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The Role of Directionality, Heterogeneity, and Correlations in Epidemic Risk and Spread
SIAM Review ( IF 10.2 ) Pub Date : 2023-05-09 , DOI: 10.1137/20m1383811 Antoine Allard , Cristopher Moore , Samuel V. Scarpino , Benjamin M. Althouse , Laurent Hébert-Dufresne
SIAM Review ( IF 10.2 ) Pub Date : 2023-05-09 , DOI: 10.1137/20m1383811 Antoine Allard , Cristopher Moore , Samuel V. Scarpino , Benjamin M. Althouse , Laurent Hébert-Dufresne
SIAM Review, Volume 65, Issue 2, Page 471-492, May 2023.
Most models of epidemic spread, including many designed specifically for COVID-19, implicitly assume mass-action contact patterns and undirected contact networks, meaning that the individuals most likely to spread the disease are also the most at risk of contracting it from others. Here, we review results from the theory of random directed graphs which show that many important quantities, including the reproduction number and the epidemic size, depend sensitively on the joint distribution of in- and out-degrees (``risk” and “spread''), including their heterogeneity and the correlation between them. By considering joint distributions of various kinds, we elucidate why some types of heterogeneity cause a deviation from the standard Kermack--McKendrick analysis of SIR models, i.e., so-called mass-action models where contacts are homogeneous and random, and why some do not. We also show that some structured SIR models informed by realistic complex contact patterns among types of individuals (age or activity) are simply mixtures of Poisson processes and tend not to deviate significantly from the simplest mass-action model. Finally, we point out some possible policy implications of this directed structure, both for contact tracing strategy and for interventions designed to prevent superspreading events. In particular, directed graphs have a forward and a backward version of the classic “friendship paradox''---forward edges tend to lead to individuals with high risk, while backward edges lead to individuals with high spread---such that a combination of both forward and backward contact tracing is necessary to find superspreading events and prevent future cascades of infection.
中文翻译：
方向性、异质性和相关性在流行病风险和传播中的作用
SIAM Review，第 65 卷，第 2 期，第 471-492 页，2023 年 5 月。
大多数流行病传播模型，包括许多专门为 COVID-19 设计的模型，都隐含地假设了大规模行动接触模式和无向接触网络，这意味着最有可能传播该疾病的个人也最有可能被他人感染。在这里，我们回顾了随机有向图理论的结果，这些结果表明许多重要的数量，包括繁殖数量和流行病规模，敏感地依赖于入度和出度的联合分布（“风险”和“传播” '），包括它们的异质性和它们之间的相关性。通过考虑各种联合分布，我们阐明了为什么某些类型的异质性会导致偏离 SIR 模型的标准 Kermack-McKendrick 分析，即，所谓的质量作用模型，其中接触是均匀和随机的，为什么有些不是。我们还表明，一些结构化的 SIR 模型由不同类型的个体（年龄或活动）之间的现实复杂接触模式提供信息，它们只是泊松过程的混合体，往往不会显着偏离最简单的质量作用模型。最后，我们指出了这种定向结构的一些可能的政策影响，包括接触者追踪策略和旨在防止超级传播事件的干预措施。特别是，有向图具有经典“友谊悖论”的正向和反向版本——正向边往往会导致高风险个体，
更新日期：2023-05-08
Most models of epidemic spread, including many designed specifically for COVID-19, implicitly assume mass-action contact patterns and undirected contact networks, meaning that the individuals most likely to spread the disease are also the most at risk of contracting it from others. Here, we review results from the theory of random directed graphs which show that many important quantities, including the reproduction number and the epidemic size, depend sensitively on the joint distribution of in- and out-degrees (``risk” and “spread''), including their heterogeneity and the correlation between them. By considering joint distributions of various kinds, we elucidate why some types of heterogeneity cause a deviation from the standard Kermack--McKendrick analysis of SIR models, i.e., so-called mass-action models where contacts are homogeneous and random, and why some do not. We also show that some structured SIR models informed by realistic complex contact patterns among types of individuals (age or activity) are simply mixtures of Poisson processes and tend not to deviate significantly from the simplest mass-action model. Finally, we point out some possible policy implications of this directed structure, both for contact tracing strategy and for interventions designed to prevent superspreading events. In particular, directed graphs have a forward and a backward version of the classic “friendship paradox''---forward edges tend to lead to individuals with high risk, while backward edges lead to individuals with high spread---such that a combination of both forward and backward contact tracing is necessary to find superspreading events and prevent future cascades of infection.
中文翻译：
方向性、异质性和相关性在流行病风险和传播中的作用
SIAM Review，第 65 卷，第 2 期，第 471-492 页，2023 年 5 月。
大多数流行病传播模型，包括许多专门为 COVID-19 设计的模型，都隐含地假设了大规模行动接触模式和无向接触网络，这意味着最有可能传播该疾病的个人也最有可能被他人感染。在这里，我们回顾了随机有向图理论的结果，这些结果表明许多重要的数量，包括繁殖数量和流行病规模，敏感地依赖于入度和出度的联合分布（“风险”和“传播” '），包括它们的异质性和它们之间的相关性。通过考虑各种联合分布，我们阐明了为什么某些类型的异质性会导致偏离 SIR 模型的标准 Kermack-McKendrick 分析，即，所谓的质量作用模型，其中接触是均匀和随机的，为什么有些不是。我们还表明，一些结构化的 SIR 模型由不同类型的个体（年龄或活动）之间的现实复杂接触模式提供信息，它们只是泊松过程的混合体，往往不会显着偏离最简单的质量作用模型。最后，我们指出了这种定向结构的一些可能的政策影响，包括接触者追踪策略和旨在防止超级传播事件的干预措施。特别是，有向图具有经典“友谊悖论”的正向和反向版本——正向边往往会导致高风险个体，
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