Department of Visceral Surgery and Medicine, Inselspital, Bern University Hospital, University of Bern, Bern, Switzerland.
Multidisciplinary Center for Infectious Diseases, University of Bern, Bern, Switzerland.
Bull Math Biol. 2024 Feb 1;86(3):27. doi: 10.1007/s11538-023-01249-x.
Understanding disease transmission in the workplace is essential for protecting workers. To model disease outbreaks, the small populations in many workplaces require that stochastic effects are considered, which results in higher uncertainty. The aim of this study was to quantify and interpret the uncertainty inherent in such circumstances. We assessed how uncertainty of an outbreak in workplaces depends on i) the infection dynamics in the community, ii) the workforce size, iii) spatial structure in the workplace, iv) heterogeneity in susceptibility of workers, and v) heterogeneity in infectiousness of workers. To address these questions, we developed a multiscale model: A deterministic model to predict community transmission, and a stochastic model to predict workplace transmission. We extended this basic workplace model to allow for spatial structure, and heterogeneity in susceptibility and infectiousness in workers. We found a non-monotonic relationship between the workplace transmission rate and the coefficient of variation (CV), which we use as a measure of uncertainty. Increasing community transmission, workforce size and heterogeneity in susceptibility decreased the CV. Conversely, increasing the level of spatial structure and heterogeneity in infectiousness increased the CV. However, when the model predicts bimodal distributions, for example when community transmission is low and workplace transmission is high, the CV fails to capture this uncertainty. Overall, our work informs modellers and policy makers on how model complexity impacts outbreak uncertainty. In particular: workforce size, community and workplace transmission, spatial structure and individual heterogeneity contribute in a specific and individual manner to the predicted workplace outbreak size distribution.
了解工作场所中的疾病传播对于保护工人至关重要。为了对疾病爆发进行建模，许多工作场所中的小群体需要考虑随机效应，这会导致更高的不确定性。本研究的目的是量化和解释这种情况下固有的不确定性。我们评估了工作场所中爆发的不确定性如何取决于 i）社区中的感染动态，ii）劳动力规模，iii）工作场所中的空间结构，iv）工人易感性的异质性，以及 v）工人传染性的异质性。为了解决这些问题，我们开发了一个多尺度模型：一个确定性模型来预测社区传播，和一个随机模型来预测工作场所传播。我们扩展了这个基本的工作场所模型，以允许存在空间结构以及工人易感性和传染性的异质性。我们发现工作场所传播率与变异系数（CV）之间存在非单调关系，我们将 CV 用作不确定性的度量。社区传播、劳动力规模和易感性异质性的增加降低了 CV。相反，空间结构和传染性异质性水平的增加增加了 CV。然而，当模型预测双峰分布时，例如当社区传播较低而工作场所传播较高时，CV 无法捕捉到这种不确定性。总的来说，我们的工作为建模者和决策者提供了关于模型复杂性如何影响爆发不确定性的信息。特别是：劳动力规模、社区和工作场所传播、空间结构和个体异质性以特定和个体的方式对预测的工作场所爆发规模分布做出贡献。
