论文标题
在配置模型网络上精确关闭流行方程的必要条件
Necessary and sufficient conditions for exact closures of epidemic equations on configuration model networks
论文作者
论文摘要
我们证明，当且仅当程度分布是泊松，二项式或负二项式时，才有可能在配置模型网络上的成对流行方程的确切关闭。证明依赖于建立这些特定程度分布，封闭成对模型的等效性和所谓的动态生存分析（DSA）基于边缘模型，该模型先前被证明是准确的。确实，正如我们在这里显示的那样，DSA模型等同于众所周知的基于边缘的VOLZ模型。我们使用此结果将封闭的成对模型和VOLZ模型减少到仅涉及易感的同一单程方程，该方程在感染时代具有有用的统计解释。我们用一些数字示例来说明我们的发现。
We prove that the exact closure of SIR pairwise epidemic equations on a configuration model network is possible if and only if the degree distribution is Poisson, Binomial, or Negative Binomial. The proof relies on establishing, for these specific degree distributions, the equivalence of the closed pairwise model and the so-called dynamical survival analysis (DSA) edge-based model which was previously shown to be exact. Indeed, as we show here, the DSA model is equivalent to the well-known edge-based Volz model. We use this result to provide reductions of the closed pairwise and Volz models to the same single equation involving only susceptibles, which has a useful statistical interpretation in terms of the times to infection. We illustrate our findings with some numerical examples.
