Department of Engineering Mathematics, University of Bristol, Bristol, UK.
Department of Statistics, Athens University of Economics and Business, Athens, Greece.
Stat Med. 2024 Oct 15;43(23):4542-4558. doi: 10.1002/sim.10195. Epub 2024 Aug 9.
Despite the progress in medical data collection the actual burden of SARS-CoV-2 remains unknown due to under-ascertainment of cases. This was apparent in the acute phase of the pandemic and the use of reported deaths has been pointed out as a more reliable source of information, likely less prone to under-reporting. Since daily deaths occur from past infections weighted by their probability of death, one may infer the total number of infections accounting for their age distribution, using the data on reported deaths. We adopt this framework and assume that the dynamics generating the total number of infections can be described by a continuous time transmission model expressed through a system of nonlinear ordinary differential equations where the transmission rate is modeled as a diffusion process allowing to reveal both the effect of control strategies and the changes in individuals behavior. We develop this flexible Bayesian tool in Stan and study 3 pairs of European countries, estimating the time-varying reproduction number ( ) as well as the true cumulative number of infected individuals. As we estimate the true number of infections we offer a more accurate estimate of . We also provide an estimate of the daily reporting ratio and discuss the effects of changes in mobility and testing on the inferred quantities.
尽管在医学数据收集方面取得了进展，但由于病例未被充分确定，实际的 SARS-CoV-2 负担仍然未知。这在大流行的急性期是显而易见的，并且已经指出报告的死亡人数是更可靠的信息来源，不太可能报告不足。由于每日死亡人数是过去感染的加权概率，因此可以根据报告的死亡人数推断出按年龄分布的总感染人数。我们采用这种框架，并假设产生总感染人数的动力学可以通过一个连续时间传播模型来描述，该模型通过一个非线性常微分方程组来表示，其中传播率被建模为一个扩散过程，这使得既能揭示控制策略的效果，也能揭示个体行为的变化。我们在 Stan 中开发了这个灵活的贝叶斯工具，并研究了 3 对欧洲国家，估计了时变繁殖数 ( ) 以及真实的累计感染人数。由于我们估计了真实的感染人数，因此可以更准确地估计 。我们还提供了每日报告比例的估计，并讨论了流动性和检测变化对推断数量的影响。
