Centre de mathématiques appliquées (CMAP), Ecole Polytechnique, Palaiseau, 91128, France.
MaIAGE, INRAE, Université Paris-Saclay, Jouy-en-Josas, 78350, France.
J Math Biol. 2024 Sep 30;89(4):45. doi: 10.1007/s00285-024-02147-z.
Models with several levels of mixing (households, workplaces), as well as various corresponding formulations for , have been proposed in the literature. However, little attention has been paid to the impact of the distribution of the population size within social structures, effect that can help plan effective interventions. We focus on the influence on the model outcomes of teleworking strategies, consisting in reshaping the distribution of workplace sizes. We consider a stochastic SIR model with two levels of mixing, accounting for a uniformly mixing general population, each individual belonging also to a household and a workplace. The variance of the workplace size distribution appears to be a good proxy for the impact of this distribution on key outcomes of the epidemic, such as epidemic size and peak. In particular, our findings suggest that strategies where the proportion of individuals teleworking depends sublinearly on the size of the workplace outperform the strategy with linear dependence. Besides, one drawback of the model with multiple levels of mixing is its complexity, raising interest in a reduced model. We propose a homogeneously mixing SIR ODE-based model, whose infection rate is chosen as to observe the growth rate of the initial model. This reduced model yields a generally satisfying approximation of the epidemic. These results, robust to various changes in model structure, are very promising from the perspective of implementing effective strategies based on social distancing of specific contacts. Furthermore, they contribute to the effort of building relevant approximations of individual based models at intermediate scales.
文献中提出了具有多个混合层次（家庭、工作场所）的模型，以及各种相应的 公式。然而，人们很少关注人口规模在社会结构内分布的影响，这种影响有助于规划有效的干预措施。我们专注于远程办公策略对模型结果的影响，这些策略包括重塑工作场所规模的分布。我们考虑了一个具有两个混合层次的随机 SIR 模型，该模型考虑了均匀混合的总人口，每个个体也属于一个家庭和一个工作场所。工作场所规模分布的方差似乎是衡量这种分布对流行病关键结果（如流行病规模和峰值）影响的一个很好的指标。特别是，我们的研究结果表明，个体远程办公的比例与工作场所规模呈次线性依赖的策略优于线性依赖的策略。此外，具有多个混合层次的模型的一个缺点是其复杂性，这引发了对简化模型的兴趣。我们提出了一个基于均相混合 SIR ODE 的模型，其感染率被选为观察初始模型增长率的指标。该简化模型对流行病进行了普遍令人满意的近似。这些结果对于基于特定接触者的社交距离实施有效策略具有很强的前景，并且对模型结构的各种变化具有稳健性。此外，它们有助于构建个体为基础的模型在中间尺度上的相关近似。
