Hägerstrand's time geography is a powerful conceptual framework for understanding constraints on human activity participation in space and time. However, rigorous, analytical definitions of basic time geography entities and relationships do not exist. This limits abilities to make statements about error and uncertainty in time geographic measurement and analysis. It also compromises comparison among different time geographic analyses and the development of standard time geographic computational tools. The time geographic measurement theory in this article consists of analytical formulations for basic time geography entities and relations, specifically, the spacetime path, prism, composite path-prisms, stations, bundling, and intersections. The definitions have arbitrary spatial and temporal resolutions and are explicit with respect to informational assumptions: there are clear distinctions between measured and inferred components of each entity or relation. They are also general to n-dimensional space rather than the strict two-dimensional space of classical time geography. Algebraic solutions are available for one or two spatial dimensions, while numeric (but tractable) solutions are required for some entities and relations in higher dimensional space.
The COVID-19 pandemic and related restrictions led to major transit demand decline for many public transit systems in the United States. This paper is a systematic analysis of the dynamics and dimensions of this unprecedented decline. Using transit demand data derived from a widely used transit navigation app, we fit logistic functions to model the decline in daily demand and derive key parameters: base value, the apparent minimal level of demand and cliff and base points, representing the initial date when transit demand decline began and the final date when the decline rate attenuated. Regression analyses reveal that communities with higher proportions of essential workers, vulnerable populations (African American, Hispanic, Female, and people over 45 years old), and more coronavirus Google searches tend to maintain higher levels of minimal demand during COVID-19. Approximately half of the agencies experienced their decline before the local spread of COVID-19 likely began; most of these are in the US Midwest. Almost no transit systems finished their decline periods before local community spread. We also compare hourly demand profiles for each system before and during COVID-19 using ordinary Procrustes distance analysis. The results show substantial departures from typical weekday hourly demand profiles. Our results provide insights into public transit as an essential service during a pandemic.
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