Title: Modeling Study: Characterizing the Spatial Heterogeneity of the COVID-19 Pandemic through Shape Analysis of Epidemic Curves.

Background : The COVID-19 incidence rates across different geographical regions (e.g., counties in a state, states in a nation, countries in a continent) follow different shapes and patterns. The overall summaries at coarser spatial scales, that are obtained by simply averaging individual curves (across regions), hide nuanced variability and blur the spatial heterogeneity at finer spatial scales. For instance, a decreasing incidence rate curve in one region is obscured by an increasing rate curve for another region, when the analysis relies on coarse averages of locally heterogeneous transmission dynamics. Objective : To highlight regional differences in COVID-19 incidence rates and to discover prominent patterns in shapes of incidence rate curves in multiple regions (USA and Europe). Methods : We employ statistical methods to analyze shapes of local COVID-19 incidence rate curves and statistically group them into distinct clusters, according to their shapes. Using this information, we derive the so-called shape averages of curves within these clusters, which represent the dominant incidence patterns of these clusters. We apply this methodology to the analysis of the daily incidence trajectory of the COVID-pandemic for two geographic areas: A state-level analysis within the USA and a country-level analysis within Europe during late-February to October 1 st , 2020. Results : Our analyses reveal that pandemic curves often differ substantially across regions. However, there are only a handful of shapes that dominate transmission dynamics for all states in the USA and countries in Europe. This approach yields a broad classification of spatial areas into different characteristic epidemic trajectories. In particular, spatial areas within the same cluster have followed similar transmission and control dynamics. Conclusion : The shape-based analysis of pandemic curves presented here helps divide country or continental data into multiple regional clusters, each cluster containing areas with similar trend patterns. This clustering helps highlight differences in pandemic curves across regions and provides summaries that better reflect dynamical patterns within the clusters. This approach adds to the methodological toolkit for public health practitioners to facilitate decision making at different spatial scales.