COVID-19: Bayesian inference for high resolution stochastic modelling for the UK

我们将开发一个有效和强大的MCMC为基础的框架，完全贝叶斯推理方法的空间明确的，随机的，部分观察到的元人口流行病模型在人群中。这将适用于目前英国的Covid-19疫情。我们特别关注的挑战是，面对删失数据观察，提供持续更新的参数估计和风险评估，从而对英国Covid-19患病率和发病率进行详细的年龄和空间特定预测。我们的预测将针对疾病管理，提供流行病死灰复燃的空间“热点”预警，作为行为和社会干预措施。（封锁）措施被解除，以及通知有针对性的疾病监测，以空间和年龄相关的亚群。我们回应的观察，现有的微分方程为基础的模型通知SAGE不能在高人口分辨率，因为随着元种群变小，流行病过程固有的随机波动开始支配病例观察噪声。虽然确实存在COVID-19传播的随机模型（基于先前存在的流感模型），但在数据可用性不断变化的情况下，需要开发大规模拟合这些模型的方法。为了解决这个问题，我们将扩展我们现有的贝叶斯方法，以实时风险预测的个人水平的模型，开发一个数据增强MCMC方法定义的高维元人口结构的状态转换模型。推理和前向模拟算法将使用谷歌的TensorFlow库构建，在快速算法开发和快速GPU加速计算之间提供适当的平衡，以确保我们的结果及时，并适用于英国各地的Covid-19决策支持。

We will develop an efficient and robust MCMC-based framework for fully Bayesian inference methodology for spatially explicit, stochastic, and partially observed meta-population epidemic models within human populations. This will be applied to the current UK Covid-19 epidemic. We particularly focus on the challenge of providing continuously updated parameter estimation and risk assessment in the face of censored data observations and hence detailed age- and space-specific predictions of Covid-19 prevalence and incidence in the UK. Our predictions will be targeted at disease management, providing early warning of spatial "hotspots" of epidemic resurgence as Behavioural and Social Intervention (lockdown) measures are lifted, as well as informing targeted disease surveillance to space- and age-related sub-populations.We respond to the observation that existing differential equation based models informing SAGE cannot operate at high population resolution, since as meta-populations get smaller, stochastic fluctuations intrinsic to the epidemic process begin to dominate case observation noise. Whilst stochastic models of Covid-19 spread (based on pre-existing influenza models) do exist, methods to fit them at scale in the face of changing data availability require development. To address this, we will extend our existing Bayesian approach to real-time risk prediction for individual level models, developing a data-augmentation MCMC approach to state-transition models defined on high-dimensional meta-population structures. Inference and forward simulation algorithms will be built using Google's TensorFlow library, providing appropriate balance between rapid algorithm development and fast GPU-accelerated computations to ensure that our results are timely, and appropriate for Covid-19 decision support across the UK.