The dynamics of the spread of epidemics, such as the recent outbreak of the SARS-CoV-2 virus, is highly nonlinear and therefore difficult to predict. As time evolves in the present pandemic, it appears more and more clearly that a clustered dynamics is a key element of the description. This means that the disease rapidly evolves within spatially localized networks, that diffuse and eventually create new clusters. We improve upon the simplest possible compartmental model, the SIR model, by adding an additional compartment associated with the clustered individuals. This sophistication is compatible with more advanced compartmental models and allows, at the lowest level of complexity, to leverage the well-mixedness assumption. The so-obtained SBIR model takes into account the effect of inhomogeneity on epidemic spreading, and compares satisfactorily with results on the pandemic propagation in a number of European countries, during and immediately after lock-down. Especially, the decay exponent of the number of new cases after the first peak of the epidemic is captured without the need to vary the coefficients of the model with time. We show that this decay exponent is directly determined by the diffusion of the ensemble of clustered individuals and can be related to a global reproduction number, that overrides the classical, local reproduction number.

流行病传播的动态，例如最近爆发的 SARS-CoV-2 病毒，是高度非线性的，因此难以预测。随着当前大流行中时间的推移，越来越清楚地表明，集群动态是描述的关键要素。这意味着该疾病在空间局部网络中迅速发展，扩散并最终产生新的集群。我们通过添加与聚类个体相关的额外隔间来改进最简单的隔间模型，即 SIR 模型。这种复杂性与更高级的隔间模型兼容，并允许以最低的复杂度利用混合良好的假设。如此获得的 SBIR 模型考虑了不均匀性对流行病传播的影响，并与一些欧洲国家在封锁期间和封锁后立即传播的结果进行了令人满意的比较。特别是，无需随时间改变模型的系数，即可捕获流行病第一个高峰后新病例数的衰减指数。我们表明，这种衰减指数直接由聚集个体的集合的扩散决定，并且可以与覆盖经典的局部再生数的全局再生数相关。