Inferring epidemic characteristics with networks

贝叶斯模型比较自然地在统计物理背景下被解释。我们表明，认真对待这种解释会极大地减少计算工作量。鉴于将观察到的大流行表现转化为对病毒传播和感染过程的了解的复杂性，我们选择了一种简单的数据驱动方法，考虑到人口年龄分布和死亡率的年龄相关性。虽然我们方法的概念基础很简单，但我们必须克服计算困难，才能使实现符合有限计算资源的可计算性。我们的结果经过检验，不依赖于我们模拟的网络的大小，不依赖于我们为每个模型使用的随机运行的数量，也不依赖于我们用于线性回归的天数。 我们可以预测首次感染时间的后验分布，TimeFirstDeath。动态模型可以预测首次感染后的感染人数和相对于首次死亡时间的人数，因为我们在分析中没有使用感染或康复统计数据。请注意，同一参数集的感染数量存在巨大差异，部分原因是网络本身的随机性。 在感染的内在参数保持不变的情况下，我们可以通过改变网络连接来预测不同程度的社会距离的影响。我们假设网络中一定比例的节点会遵守社会距离，并且只有这些遵守规则的节点会随机减少一定比例的连接。有趣的是，虽然实现社交距离的顺从节点的比例与累积死亡人数的平坦化相关，但更重要的参数似乎是顺从节点的社交距离程度，在当前上下文中，这意味着网络中仅为模拟社交距离而随机删除的网络中的边的比例。在没有社会距离的情况下，感染人数的指数增长速度为每天0.18美元。03美元。这一价格降至每天约0.08美元。 即使是最悲观的社会疏远效果。虽然0.03美元的不确定性可能看起来不是很大，但它出现在指数级，并导致预测的感染人数的巨大范围，这是一个非常感兴趣的主题，因为病毒可能无症状传播。考虑到这一点，仅关注每天0.18美元的平均值就意味着，如果在第25天第一个死亡后两周开始社交距离，那么从一个感染者开始的100日内，这样的接触减少相当于6,500万对166000感染者。

Bayesian model comparison is naturally interpreted in a statistical physics context. We showed that taking this interpretation seriously leads to enormous reductions in computational effort. Given the complexity of translating the observed manifestations of the pandemic into an understanding of the virus's spread and the course of the infection, we opted for a simple data-driven approach, taking into account population age distributions and the age dependence of the death rate. While the conceptual basis of our approach is simple, there were computational difficulties we had to overcome to make the implementation amenable to computability with finite computational resources. Our results were checked to not depend on the size of the networks we simulated, on the number of stochastic runs we used for each model, nor on the number of days that we used for the linear regression. We can predict the posterior distribution of time of initial infection, TimeFirstDeath. The dynamic model can predict the number of people infected after the first infection and relative to the time of first death because we made no use of infection or recovery statistics in our analysis. Note the enormous variation in the number of infections for the same parameter set, only partly due to stochasticity of the networks themselves. With parameters intrinsic to the infection held fixed, we can predict the effect of various degrees of social distancing by varying network connectivity. We assumed that a certain fraction of nodes in the network would comply with social distancing and only these compliant nodes would reduce their connections at random by a certain fraction. Interestingly, while the fraction of compliant nodes that implement social distancing is relevant to the flattening of the cumulative number of deaths, the more important parameter appears to be the degree of social distancing by the compliant nodes, which in the present context means the fraction of edges in the network that are randomly deleted for compliant nodes only to simulate social distancing. The rate of exponential increase in the number of infected individuals is $0.18pm .03$ per day without social distancing. This rate falls to about $0.08$ per day with even the most pessimistic social-distancing effectuation. While the uncertainty of $0.03$ may not appear to be large, it appears in an exponent and leads to enormous ranges in the predicted number of infected individuals, a subject of great interest given possible asymptomatic transmission of the virus. With this caveat in mind, just focusing on the mean value $0.18$ per day implies that such a contact reduction corresponds to 65 million vs. 166000 infected individuals after a period of 100 days starting from one infected individual if social distancing is initiated two weeks after the first death on day 25.