We tackle limitations of ordinary differential equation-driven Susceptible-Infections-Removed (SIR) models and their extensions that have recently be employed for epidemic nowcasting and forecasting. In particular, we deal with challenges related to the extension of SIR-type models to account for the so-called \textit{environmental stochasticity}, i.e., external factors, such as seasonal forcing, social cycles and vaccinations that can dramatically affect outbreaks of infectious diseases. Typically, in SIR-type models environmental stochasticity is modelled through stochastic processes. However, this stochastic extension of epidemic models leads to models with large dimension that increases over time. Here we propose a Bayesian approach to build an efficient modelling and inferential framework for epidemic nowcasting and forecasting by using Gaussian Markov random fields to model the evolution of these stochastic processes over time and across population strata. Importantly, we also develop a bespoke and computationally efficient Markov chain Monte Carlo algorithm to estimate the large number of parameters and latent states of the proposed model. We test our approach on simulated data and we apply it to real data from the Covid-19 pandemic in the United Kingdom.

翻译：我们解决了常微分方程驱动的易感-感染-移除（SIR）模型及其扩展在近期用于流行病即时预测与预报时存在的局限性。具体而言，我们应对了将SIR类模型扩展以纳入所谓“环境随机性”所带来的挑战，即季节性强迫、社会周期和疫苗接种等能显著影响传染病暴发的外部因素。在SIR类模型中，环境随机性通常通过随机过程进行建模。然而，这种流行病模型的随机扩展会导致模型维度庞大且随时间增长。本文提出一种贝叶斯方法，通过使用高斯马尔可夫随机场来建模这些随机过程随时间及跨人口层级的演化，从而构建一个用于流行病即时预测与预报的高效建模与推断框架。重要的是，我们还开发了一种定制化的计算高效马尔可夫链蒙特卡洛算法，用于估计所提出模型的大量参数与潜变量状态。我们在模拟数据上验证了该方法，并将其应用于英国新冠疫情的真实数据。