论文标题
估算对SARS-COV-2的免疫力之前所需的“锁定”周期：在包括英国和爱尔兰在内的七个欧洲国家，基于模型的易感人群规模“ S0”的分析
Estimating required 'lockdown' cycles before immunity to SARS-CoV-2: Model-based analyses of susceptible population sizes, 'S0', in seven European countries including the UK and Ireland
论文作者
论文摘要
我们使用贝叶斯模型反转来估算从2020年1月下旬到2020年4月5日的数据，从报告的病例和七个国家的死亡率进行估计流行参数。采用了两种不同的生成模型类型：首先是连续的时间动态系统实施易感性暴露于暴露于现象的模型（SEIR）模型（SEIR）的模型（SEER）的模型（SEER）或固定的Markswistion（Seect）（Markov）（Markov）（Markov）（Markov）或HER（MARK）（MD）（MD）HER（MDP）HER（MDP）MDP（MDP）MDP（MDP） SEIR模型。两种模型都将初始易感人群（S0）以及流行参数的大小进行参数。参数估计（数据拟合）是使用标准贝叶斯方案（变分拉普拉斯）进行的，旨在允许模型参数的潜在不可观察的状态和不确定性。 两种模型都概括了案例和死亡率给出的传播和疾病的动态。预计目前波浪的高峰是过去的四个国家（意大利，西班牙，德国和瑞士），在爱尔兰的0.5-2周中出现，在英国出现1-3周。对于法国，一种模型估计了过去一周内的峰值，而将来将在两周内将来。至关重要的是，在连续时间和HMM模型下，每个国家 /地区的最大后验（MAP）估计值表示有效的人口量低于20％（总人口大小）。在所有七个国家和两个模型中，贝叶斯的加权平均水平都达到了平均水平，我们估计总人口的6.4％是免疫的。从这两种模型中，估计有效人口的最高百分比估计为英国总人口的19.6％，爱尔兰为16.7％，意大利为11.4％，西班牙为12.8％，法国为18.8％，德国为4.7％，瑞士为12.9％。 我们的结果表明，在当前浪潮之后，总人口的很大一部分将保持无免疫力。
We used Bayesian model inversion to estimate epidemic parameters from the reported case and death rates from seven countries using data from late January 2020 to April 5th 2020. Two distinct generative model types were employed: first a continuous time dynamical-systems implementation of a Susceptible-Exposed-Infectious-Recovered (SEIR) model and second: a partially observable Markov Decision Process (MDP) or hidden Markov model (HMM) implementation of an SEIR model. Both models parameterise the size of the initial susceptible population (S0), as well as epidemic parameters. Parameter estimation (data fitting) was performed using a standard Bayesian scheme (variational Laplace) designed to allow for latent unobservable states and uncertainty in model parameters. Both models recapitulated the dynamics of transmissions and disease as given by case and death rates. The peaks of the current waves were predicted to be in the past for four countries (Italy, Spain, Germany and Switzerland) and to emerge in 0.5-2 weeks in Ireland and 1-3 weeks in the UK. For France one model estimated the peak within the past week and the other in the future in two weeks. Crucially, Maximum a posteriori (MAP) estimates of S0 for each country indicated effective population sizes of below 20% (of total population size), under both the continuous time and HMM models. With a Bayesian weighted average across all seven countries and both models, we estimated that 6.4% of the total population would be immune. From the two models the maximum percentage of the effective population was estimated at 19.6% of the total population for the UK, 16.7% for Ireland, 11.4% for Italy, 12.8% for Spain, 18.8% for France, 4.7% for Germany and 12.9% for Switzerland. Our results indicate that after the current wave, a large proportion of the total population will remain without immunity.
