Nonparametric estimation and inference for spatiotemporal epidemic models

Epidemic modelling is an essential tool to understand the spread of the novel coronavirus and ultimately assist in disease prevention, policymaking, and resource allocation. In this article, we establish a state-of-the-art interface between classic mathematical and statistical models and propose a novel space-time epidemic modelling framework to study the spatial-temporal pattern in the spread of infectious diseases. We propose a quasi-likelihood approach via the penalised spline approximation and alternatively reweighted least-squares technique to estimate the model. The proposed estimators are consistent, and the asymptotic normality is established for the constant coefficients. Utilizing spatiotemporal analysis, our proposed model enhances the dynamics of the epidemiological mechanism and dissects the spatiotemporal structure of the spreading disease. We evaluate the numerical performance of the proposed method through a simulation example. Finally, we apply the proposed method in the study of the devastating COVID-19 pandemic.

传染病建模是理解新型冠状病毒传播规律、助力疾病防控、政策制定与资源调配的核心工具。本文首先搭建了经典数学模型与统计模型间的前沿衔接范式，并提出一种全新的时空传染病建模框架，用于解析传染病传播的时空特征。我们采用基于惩罚样条近似与交替重加权最小二乘技术的拟似然方法完成模型参数估计，所提出的估计量具备相合性，且针对常系数建立了渐近正态性理论。借助时空分析手段，所提模型能够完善传染病传播机制的动力学刻画，并解析传染病的时空传播结构。我们通过仿真实验评估了所提方法的数值性能。最后，我们将所提方法应用于极具破坏性的新型冠状病毒肺炎（COVID-19）大流行疫情研究中。