EPSRC Centre for Doctoral Training in Fluid Dynamics, University of Leeds, Leeds, UK.
School of Civil Engineering, University of Leeds, Leeds, UK.
Risk Anal. 2024 Sep;44(9):2125-2147. doi: 10.1111/risa.14295. Epub 2024 Mar 19.
The Wells-Riley model has been widely used to estimate airborne infection risk, typically from a deterministic point of view (i.e., focusing on the average number of infections) or in terms of a per capita probability of infection. Some of its main limitations relate to considering well-mixed air, steady-state concentration of pathogen in the air, a particular amount of time for the indoor interaction, and that all individuals are homogeneous and behave equally. Here, we revisit the Wells-Riley model, providing a mathematical formalism for its stochastic version, where the number of infected individuals follows a Binomial distribution. Then, we extend the Wells-Riley methodology to consider transient behaviours, randomness, and population heterogeneity. In particular, we provide analytical solutions for the number of infections and the per capita probability of infection when: (i) susceptible individuals remain in the room after the infector leaves, (ii) the duration of the indoor interaction is random/unknown, and (iii) infectors have heterogeneous quanta production rates (or the quanta production rate of the infector is random/unknown). We illustrate the applicability of our new formulations through two case studies: infection risk due to an infectious healthcare worker (HCW) visiting a patient, and exposure during lunch for uncertain meal times in different dining settings. Our results highlight that infection risk to a susceptible who remains in the space after the infector leaves can be nonnegligible, and highlight the importance of incorporating uncertainty in the duration of the indoor interaction and the infectivity of the infector when estimating risk.
威尔斯-莱利模型已被广泛用于估计空气传播感染的风险，通常从确定性的角度考虑（即，关注平均感染人数），或者从感染的人均概率角度考虑。它的一些主要局限性涉及到空气的充分混合、空气中病原体的稳态浓度、室内相互作用的特定时间以及所有个体都是同质的并且行为相同。在这里，我们重新审视了威尔斯-莱利模型，为其随机版本提供了数学形式主义，其中感染个体的数量遵循二项式分布。然后，我们将威尔斯-莱利方法扩展到考虑瞬态行为、随机性和人口异质性。特别是，当：（i）感染者在感染者离开后仍留在房间内，（ii）室内相互作用的持续时间是随机的/未知的，以及（iii）感染者具有异质的量子产生率（或感染者的量子产生率是随机的/未知的）时，我们提供了感染人数和人均感染概率的解析解。我们通过两个案例研究说明了我们新公式的适用性：感染具有传染性的医疗保健工作者（HCW）探访患者时的风险，以及在不同用餐环境中不确定用餐时间时的午餐暴露。我们的结果强调了感染者离开后留在空间中的易感者的感染风险可能不容忽视，并强调了在估计风险时纳入室内相互作用持续时间和感染者传染性的不确定性的重要性。
