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

我们将开发一个基于MCMC的高效和健壮的框架，用于完全贝叶斯推理方法，用于空间显式的、随机的和部分观察到的人类种群内的元人口流行病模型。这将适用于目前英国的新冠肺炎疫情。我们尤其关注在面临被审查的数据观测以及因此对英国新冠肺炎流行率和发病率的详细的年龄和空间预测的情况下提供持续更新的参数估计和风险评估的挑战。我们的预测将以疾病管理为目标，随着行为和社会干预(封锁)措施的取消，为疫情死灰复燃的空间“热点”提供早期预警，并为空间和年龄相关的亚人口提供有针对性的疾病监测。我们对现有的基于微分方程的模型无法在高人口分辨率下运行的观察做出回应，因为随着元人口变小，流行病过程固有的随机波动开始主导病例观察噪声。虽然新冠肺炎传播的随机模型(基于先前存在的流感模型)确实存在，但面对不断变化的数据可获得性，需要开发按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来对单个级别的模型进行实时风险预测，开发一种用于定义在高维元种群结构上的状态转换模型的数据增强MCMC方法。推理和正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图形处理器加速计算之间提供适当的平衡，以确保我们的结果是及时的，并且适合英国各地的新冠肺炎决策支持。

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.