Early in an infectious disease outbreak, timely and accurate estimation of the basic reproduction number ($R_0$) and the serial interval (SI) is critical for understanding transmission dynamics and informing public health responses. While many methods estimate these quantities separately, and a small number jointly estimate them from incidence data, existing joint approaches are largely likelihood-based and do not fully exploit prior information. We propose a novel Bayesian framework for the joint estimation of $R_0$ and the serial interval using only case count data, implemented through a sequential Bayes approach. Our method assumes an SIR model and employs a mildly informative joint prior constructed by linking log-Gamma marginal distributions for $R_0$ and the SI via a Gaussian copula, explicitly accounting for their dependence. The prior is updated sequentially as new incidence data become available, allowing for real-time inference. We assess the performance of the proposed estimator through extensive simulation studies under correct model specification as well as under model misspecification, including when the true data come from an SEIR or SEAIR model, and under varying degrees of prior misspecification. Comparisons with the widely used White and Pagano likelihood-based joint estimator show that our approach yields substantially more precise and stable estimates of $R_0$, with comparable or improved bias, particularly in the early stages of an outbreak. Estimation of the SI is more sensitive to prior misspecification; however, when prior information is reasonably accurate, our method provides reliable SI estimates and remains more stable than the competing approach. We illustrate the practical utility of the proposed method using Canadian COVID-19 incidence data at both national and provincial levels.

翻译：在传染病暴发初期，及时准确地估计基本再生数（$R_0$）与序列间隔（SI）对于理解传播动态和指导公共卫生应对至关重要。尽管已有多种方法分别估计这两个量，也有少数方法基于发病数据对其进行联合估计，但现有的联合估计方法大多基于似然估计，未能充分利用先验信息。本文提出一种新颖的贝叶斯框架，仅利用病例计数数据对$R_0$和序列间隔进行联合估计，并通过序贯贝叶斯方法实现。我们的方法假设SIR模型，并采用一个弱信息联合先验分布——通过对$R_0$和SI的对数伽马边际分布通过高斯Copula进行连接而构建，从而显式地考虑了两者之间的相关性。随着新发病数据的获得，该先验分布被序贯更新，支持实时推断。我们通过广泛的模拟研究评估了所提出估计量的性能，包括在模型设定正确、模型设定错误（例如真实数据来自SEIR或SEAIR模型）以及不同程度先验设定错误的情况下的表现。与广泛使用的White和Pagano基于似然的联合估计方法相比，我们的方法能够显著提高$R_0$估计的精确度和稳定性，同时偏差相当或更小，尤其是在疫情早期阶段。序列间隔的估计对先验设定错误更为敏感；然而，当先验信息较为准确时，我们的方法能够提供可靠的SI估计，并且比对比方法更为稳定。我们使用加拿大国家级和省级的COVID-19发病数据，展示了所提出方法的实际应用价值。