Fine-Grid Spatial Interaction Matrices for Surveillance Models with Application to Influenza in Germany
Listed in
This article is not in any list yet, why not save it to one of your lists.Abstract
Background
Spatial models of infectious disease transmission often rely on administrative boundaries and simple measure of proximity, such as the neighbourhood order. While these methods effectively capture key aspects of disease spread, they may not fully account for nuances in transmission risk. This study introduces a new approach that defines transmission risk at the individual level and aggregates it to the district level. This approach aims to improve both forecast accuracy and the spatial resolution of risk mapping.
Method
We propose the Fine-Grid Spatial Interaction Matrix (FGSIM), which models transmission risk between districts based on distances between individuals. Five distance measures are transformed into contact intensity using a power-law function, forming a weight matrix applicable in the endemic-epidemic framework. We evaluate FGSIM using influenza data from Germany (2001–2020) and compare its performance to established methods and a simplified FGSIM variant. Forecasts for one to eight weeks ahead are assessed across four study regions using the weighted interval score (WIS) and ranked probability score (RPS).
Results
FGSIM outperforms its simplified variants and models without spatial dependence in most cases when evaluated in-sample. For one-week-ahead forecasts, a centroid-based model performs best in three of four regions (two when evaluated on the logarithmic scale). For longer-term forecasts (four or eight weeks ahead), one FGSIM model consistently outperforms most others. Risk maps at 100m resolution demonstrate the ability of FGSIM to identify high-risk areas not aligned with administrative boundaries.
Conclusion
FGSIM provides a flexible and computationally feasible approach to incorporate individual-level spatial structure into district-level infectious disease models. While established methods perform well in short-term forecasts, FGSIM demonstrates competitive performance for longer forecasting horizons. In addition, it enables fine-scale risk mapping, making it a valuable tool for public health planning beyond administrative districts.
