The time-dependent reproduction number for epidemics in heterogeneous populations.

IF 3.5 2区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES
Journal of The Royal Society Interface Pub Date : 2025-07-01 Epub Date: 2025-07-09 DOI:10.1098/rsif.2025.0095
Ioana Bouros, Robin N Thompson, David J Gavaghan, Ben Lambert
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引用次数: 0

Abstract

The time-dependent reproduction number [Formula: see text] can be used to track pathogen transmission and to assess the efficacy of interventions. This quantity can be estimated by fitting renewal equation models to time series of infectious disease case counts. These models almost invariably assume a homogeneous population. Individuals are assumed not to differ systematically in the rates at which they come into contact with others. It is also assumed that the typical time that elapses between one case and those it causes (known as the generation-time distribution) does not differ across groups. But contact patterns are known to widely differ by age and according to other demographic groupings, and infection risk and transmission rates have been shown to vary across groups for a range of directly transmitted diseases. Here, we derive from first principles a renewal equation framework which accounts for these differences in transmission across groups. We use a generalization of the classic M'Kendrick-von Foerster equation to handle populations structured into interacting groups. This system of partial differential equations allows us to derive a simple analytical expression for [Formula: see text], which involves only group-level contact patterns and infection risks. We show that the same expression emerges from both deterministic and stochastic discrete-time versions of the model and demonstrate through simulations that our [Formula: see text] expression governs the long-run fate of epidemics. Our renewal equation model provides a basis from which to account for more realistic, diverse populations in epidemiological models and opens the door to inferential approaches which use known group characteristics to estimate [Formula: see text].

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异种种群中流行病随时间变化的繁殖数。
随时间变化的繁殖数[公式:见文本]可用于跟踪病原体传播和评估干预措施的效果。这个数量可以通过将更新方程模型拟合到传染病病例数的时间序列来估计。这些模型几乎无一例外地假设人口是同质的。人们假定个人在与其他人接触的比率上没有系统差异。它还假定在一个病例和由它引起的那些病例之间的典型时间间隔(称为世代分布)在不同的组之间没有差异。但是,已知接触模式因年龄和其他人口分组而有很大差异,并且已表明,对于一系列直接传播疾病,不同群体的感染风险和传播率各不相同。在这里,我们从第一原理推导出一个更新方程框架,该框架解释了群体间传播的这些差异。我们使用经典M’kendrick -von Foerster方程的一般化来处理构成相互作用群体的群体。这个偏微分方程系统使我们能够为[公式:见文本]推导出一个简单的解析表达式,它只涉及群体层面的接触模式和感染风险。我们表明,同样的表达式出现在模型的确定性和随机离散时间版本中,并通过模拟证明,我们的[公式:见文本]表达式支配着流行病的长期命运。我们的更新方程模型为在流行病学模型中考虑更现实、更多样化的人口提供了基础,并为使用已知群体特征进行估计的推理方法打开了大门[公式:见文本]。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of The Royal Society Interface
Journal of The Royal Society Interface 综合性期刊-综合性期刊
CiteScore
7.10
自引率
2.60%
发文量
234
审稿时长
2.5 months
期刊介绍: J. R. Soc. Interface welcomes articles of high quality research at the interface of the physical and life sciences. It provides a high-quality forum to publish rapidly and interact across this boundary in two main ways: J. R. Soc. Interface publishes research applying chemistry, engineering, materials science, mathematics and physics to the biological and medical sciences; it also highlights discoveries in the life sciences of relevance to the physical sciences. Both sides of the interface are considered equally and it is one of the only journals to cover this exciting new territory. J. R. Soc. Interface welcomes contributions on a diverse range of topics, including but not limited to; biocomplexity, bioengineering, bioinformatics, biomaterials, biomechanics, bionanoscience, biophysics, chemical biology, computer science (as applied to the life sciences), medical physics, synthetic biology, systems biology, theoretical biology and tissue engineering.
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