[Paper Review] Non-stationary spatio-temporal point process modeling for high-resolution COVID-19 data

Zheng Dong, Shixiang Zhu+3 more|arXiv (Cornell University)|Sep 18, 2021

COVID-19 epidemiological studies21 references4 citations

TL;DR

This paper proposes a non-stationary spatio-temporal point process model with a neural network-based kernel to analyze high-resolution COVID-19 case data in Cali, Colombia, capturing fine-grained transmission dynamics. The model outperforms state-of-the-art methods in forecasting new cases and identifies key urban landmarks as major transmission sources, offering high interpretability and predictive accuracy for urban epidemic surveillance.

ABSTRACT

Most COVID-19 studies commonly report figures of the overall infection at a state- or county-level. This aggregation tends to miss out on fine details of virus propagation. In this paper, we analyze a high-resolution COVID-19 dataset in Cali, Colombia, that records the precise time and location of every confirmed case. We develop a non-stationary spatio-temporal point process equipped with a neural network-based kernel to capture the heterogeneous correlations among COVID-19 cases. The kernel is carefully crafted to enhance expressiveness while maintaining model interpretability. We also incorporate some exogenous influences imposed by city landmarks. Our approach outperforms the state-of-the-art in forecasting new COVID-19 cases with the capability to offer vital insights into the spatio-temporal interaction between individuals concerning the disease spread in a metropolis.

Motivation & Objective

• To model fine-grained, individual-level spatio-temporal transmission patterns of COVID-19 using high-resolution case data from Cali, Colombia.
• To address the limitations of stationary models in capturing heterogeneous transmission dynamics across urban environments.
• To incorporate exogenous influences from city landmarks known to facilitate virus spread, such as crowded or poorly ventilated areas.
• To develop a computationally efficient estimation strategy for intractable likelihoods in non-stationary point processes.
• To provide interpretable, high-accuracy forecasts that support real-time public health decision-making.

Proposed method

• The model uses a non-stationary spatio-temporal point process framework where the conditional intensity function depends on both endogenous triggering effects and exogenous landmark influences.
• A neural network parameterizes the kernel function to capture complex, location- and time-varying correlations in case occurrences, enhancing model flexibility.
• The kernel is designed to be interpretable by linking feature functions to specific spatial and temporal patterns, including landmark proximity.
• The log-likelihood function is approximated using an analytical expression to handle the intractable double integral, enabling efficient maximum likelihood estimation.
• The model integrates exogenous covariates representing city landmarks to reflect real-world transmission risks in dense or poorly ventilated zones.
• Model fitting employs a computationally efficient optimization strategy to scale to high-resolution datasets over six months.

Experimental results

Research questions

• RQ1 How can a non-stationary spatio-temporal point process model effectively capture the heterogeneous spread of COVID-19 at the individual level in an urban setting?
• RQ2 What is the role of specific city landmarks in amplifying or enabling localized transmission clusters?
• RQ3 How does incorporating neural network-based kernels improve predictive performance compared to traditional stationary or parametric kernels?
• RQ4 To what extent can the model’s interpretability be preserved while achieving high forecasting accuracy?
• RQ5 Can the model detect and forecast distinct epidemic phases, such as early spread, outbreaks, and plateau stages, in real-world data?

Key findings

• The proposed NSSTPP model achieved the lowest mean absolute error (MAE) of 2.843 in out-of-sample prediction for the last four weeks, significantly outperforming baselines like ETAS (MAE 4.908) and SIR (MAE 7.101).
• The model identified the city center, northeast, and parts of the northeast as high-risk zones, aligning with areas of greater socioeconomic vulnerability and higher population density.
• Incorporating exogenous landmarks as transmission sources improved model performance, with NSSTPP-Exo(R=3) achieving MAE 4.548, demonstrating the importance of spatial context.
• The model successfully captured four distinct pandemic stages—early spread, pre-outbreak, pre-second-outbreak, and plateau—showing spatial intensity shifts that reflect real-world transmission dynamics.
• The predicted conditional intensity maps visually aligned with actual case locations, showing higher risk in densely populated and underserved communes, and lower risk in wealthier southern areas.
• The model’s interpretability was enhanced by linking neural network features to physical locations, enabling public health officials to identify and target high-risk zones with precision.