PDF(Pubmed)
Abstract：
During the recent COVID-19 pandemic, the instantaneous reproduction number, R(t), has surged as a widely used measure to target public health interventions aiming at curbing the infection rate. In analogy with the basic reproduction number that arises from the linear stability analysis, R(t) is typically interpreted as a threshold parameter that separates exponential growth (R(t) > 1) from exponential decay (R(t) < 1). In real epidemics, however, the finite number of susceptibles, the stratification of the population (e.g. by age or vaccination state), and heterogeneous mixing lead to more complex epidemic courses. In the context of the multidimensional renewal equation, we generalize the scalar R(t) to a reproduction matrix, [Formula: see text], which details the epidemic state of the stratified population, and offers a concise epidemic forecasting scheme. First, the reproduction matrix is computed from the available incidence data (subject to some a priori assumptions), then it is projected into the future by a transfer functional to predict the epidemic course. We demonstrate that this simple scheme allows realistic and accurate epidemic trajectories both in synthetic test cases and with reported incidence data from the COVID-19 pandemic. Accounting for the full heterogeneity and nonlinearity of the infection process, the reproduction matrix improves the prediction of the infection peak. In contrast, the scalar reproduction number overestimates the possibility of sustaining the initial infection rate and leads to an overshoot in the incidence peak. Besides its simplicity, the devised forecasting scheme offers rich flexibility to be generalized to time-dependent mitigation measures, contact rate, infectivity and vaccine protection.
摘要：
在最近的COVID-19大流行期间，瞬时再现数，R(t),已成为一种广泛使用的针对旨在遏制感染率的公共卫生干预措施的措施。与线性稳定性分析产生的基本再现数类似，R(t)通常被解释为将指数增长(R(t)>1)与指数衰减(R(t)<1)分开的阈值参数。在真正的流行病中，然而,有限数量的易感物质，人口的分层（例如按年龄或疫苗接种状态），异质混合导致更复杂的流行病过程。在多维更新方程的背景下，我们将标量R(t)推广到再现矩阵，[公式:见正文],详细说明了分层人群的流行状态，并提供简明的流行病预测方案。首先,再现矩阵是根据可用的发生率数据计算的(受制于一些先验假设)，然后通过转移功能预测未来的流行过程。我们证明，这个简单的方案在合成测试病例和报告的COVID-19大流行的发病率数据中都允许现实和准确的流行轨迹。考虑到感染过程的完全异质性和非线性，繁殖矩阵改善了感染峰值的预测。相比之下,标量繁殖数高估了维持初始感染率的可能性，并导致发病率峰值超调。除了它的简单性，设计的预测方案提供了丰富的灵活性，可以推广到与时间相关的缓解措施，接触率,传染性和疫苗保护。
