Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time window, a continuous-time discrete-valued Markov process provides a natural description of the dynamics of each model component, typically taken to be the number of susceptible, exposed, infected or removed individuals. Fitting the SEIR model to time-course data is a challenging problem due incomplete observations and, consequently, the intractability of the observed data likelihood. Whilst sampling based inference schemes such as Markov chain Monte Carlo are routinely applied, their computational cost typically restricts analysis to data sets of no more than a few thousand infective cases. Instead, we develop a sequential inference scheme that makes use of a computationally cheap approximation of the most natural Markov process model. Crucially, the resulting model allows a tractable conditional parameter posterior which can be summarised in terms of a set of low dimensional statistics. This is used to rejuvenate parameter samples in conjunction with a novel bridge construct for propagating state trajectories conditional on the next observation of cumulative incidence. The resulting inference framework also allows for stochastic infection and reporting rates. We illustrate our approach using synthetic and real data applications.

翻译：流行病本质上具有随机性，随机模型为描述和分析此类现象提供了适当的方法。给定时间发病率数据（例如特定时间窗口内的新感染或移除病例数），连续时间离散值马尔可夫过程为各模型组分（通常取易感者、潜伏者、感染者或移除者的数量）的动态变化提供了自然描述。由于观测不完整及随之而来的观测数据似然难处理性，将SEIR模型拟合至时间序列数据是一个具有挑战性的问题。虽然基于采样的推断方案（如马尔可夫链蒙特卡洛）已常规应用，但其计算成本通常将分析限制在不超过数千感染病例的数据集。为此，我们开发了一种序列推断方案，该方案利用计算成本低廉的最自然马尔可夫过程模型近似。关键在于，所得模型允许一个易于处理的条件参数后验分布，该分布可用一组低维统计量进行概括。结合一种新颖的桥接构造（用于在给定下一次累积发病率观测的条件下传播状态轨迹），这被用于更新参数样本。所得推断框架还允许随机感染率和报告率。我们通过合成数据与真实数据应用展示了本方法的有效性。