Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation-based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS-CoV-2 dynamics, and apply our method to national surveillance counts from the 2013–2015 West Africa Ebola outbreak.

中文翻译：

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随机流行病模型的线性噪声近似适合部分观察到的发病率

适合发病率数据的随机流行病模型 (SEM) 对于阐明疫情动态、制定应对策略和为未来的流行病做好准备至关重要。SEM 通常使用马尔可夫跳跃过程 (MJP) 来表示处于离散感染状态的个体计数，但由于监测不完善、缺乏受试者级信息以及数据的时间粗糙性掩盖了真正的流行病，因此在计算上具有挑战性。对潜在流行过程进行分析积分是不可能的，并且由于潜在状态空间的维数和离散性，通过马尔可夫链蒙特卡罗（MCMC）进行积分很麻烦。基于模拟的计算方法可以解决 MJP 似然性的棘手问题，但对于复杂模型而言，其数值脆弱且昂贵。已经探索了用高斯密度近似 MJP 转变密度的线性噪声近似 (LNA)，用于分析大量人口环境中的患病率数据，但需要进行修改才能分析发病计数，而不假设数据呈正态分布。我们演示了如何重新参数化 SEM 以适当分析发生数据，并将 LNA 折叠到数据增强 MCMC 框架中，该框架在计算上优于确定性方法、统计方法和基于模拟的方法。当模型动力学复杂且适用于广泛的 SEM 时，我们的框架具有计算鲁棒性。我们在反映埃博拉、流感和 SARS-CoV-2 动态的模拟中评估了我们的方法，并将我们的方法应用于 2013-2015 年西非埃博拉疫情的国家监测计数。