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The tempo-spatial patterns of Covid-19 infections are a result of nested personal, societal, and political decisions that involve complicated epidemiological dynamics across overlapping spatial scales. High infection "hotspots" interspersed within regions where infections remained sporadic were ubiquitous early in the outbreak, but the spatial signature of the infection evolved to affect most regions equally, albeit with distinct temporal patterns. The sparseness of Covid-19 infections in the United States was analyzed at scales spanning from 10 to 2,600 km (county to continental scale). Spatial evolution of Covid-19 cases in the United States followed multifractal scaling. A rapid increase in the spatial correlation was identified early in the outbreak (March to April). Then, the increase continued at a slower rate and approached the spatial correlation of human population. Instead of adopting agent-based models that require tracking of individuals, a kernel-modulated approach is developed to characterize the dynamic spreading of disease in a multifractal distributed susceptible population. Multiphase Covid-19 epidemics were reasonably reproduced by the proposed kernel-modulated susceptible-infectious-recovered (SIR) model. The work explained the fact that while the reproduction number was reduced due to nonpharmaceutical interventions (e.g., masks, social distancing, etc.), subsequent multiple epidemic waves still occurred; this was due to an increase in susceptible population flow following a relaxation of travel restrictions and corollary stay-at-home orders. This study provides an original interpretation of Covid-19 spread together with a pragmatic approach that can be imminently used to capture the spatial intermittency at all epidemiologically relevant scales while preserving the "disordered" spatial pattern of infectious cases. [ABSTRACT FROM AUTHOR]

During the Deepwater Horizon disaster, a substantial fraction of the 600,000-900,000 tons of released petroleum liquid and natural gas became entrapped below the sea surface, but the quantity entrapped and the sequestration mechanisms have remained unclear. We modeled the buoyant jet of petroleum liquid droplets, gas bubbles, and entrained seawater, using 279 simulated chemical components, for a representative day (June 8, 2010) of the period after the sunken platform's riser pipe was pared at the wellhead (June 4-July 15). The model predicts that 27% of the released mass of petroleum fluids dissolved into the sea during ascent from the pared wellhead (1,505 m depth) to the sea surface, thereby matching observed volatile organic compound (VOC) emissions to the atmosphere. Based on combined results from model simulation and water column measurements, 24% of released petroleum fluid mass became channeled into a stable deep-water intrusion at 900- to 1,300-m depth, as aqueously dissolved compounds (~23%) and suspended petroleum liquid microdroplets (~0.8%). Dispersant injection at the wellhead decreased the median initial diameters of simulated petroleum liquid droplets and gas bubbles by 3.2-fold and 3.4-fold, respectively, which increased dissolution of ascending petroleum fluids by 25%. Faster dissolution increased the simulated flows of water-soluble compounds into biologically sparse deep water by 55%, while decreasing the flows of several harmful compounds into biologically rich surface water. Dispersant injection also decreased the simulated emissions of VOCs to the atmosphere by 28%, including a 2,000-fold decrease in emissions of benzene, which lowered health risks for response workers. [ABSTRACT FROM AUTHOR]

The tempo-spatial patterns of Covid-19 infections are a result of nested personal, societal, and political decisions that involve complicated epidemiological dynamics across overlapping spatial scales. High infection "hotspots" interspersed within regions where infections remained sporadic were ubiquitous early in the outbreak, but the spatial signature of the infection evolved to affect most regions equally, albeit with distinct temporal patterns. The sparseness of Covid-19 infections in the United States was analyzed at scales spanning from 10 to 2,600 km (county to continental scale). Spatial evolution of Covid-19 cases in the United States followed multifractal scaling. A rapid increase in the spatial correlation was identified early in the outbreak (March to April). Then, the increase continued at a slower rate and approached the spatial correlation of human population. Instead of adopting agent-based models that require tracking of individuals, a kernel-modulated approach is developed to characterize the dynamic spreading of disease in a multifractal distributed susceptible population. Multiphase Covid-19 epidemics were reasonably reproduced by the proposed kernel-modulated susceptible-infectious-recovered (SIR) model. The work explained the fact that while the reproduction number was reduced due to nonpharmaceutical interventions (e.g., masks, social distancing, etc.), subsequent multiple epidemic waves still occurred; this was due to an increase in susceptible population flow following a relaxation of travel restrictions and corollary stay-at-home orders. This study provides an original interpretation of Covid-19 spread together with a pragmatic approach that can be imminently used to capture the spatial intermittency at all epidemiologically relevant scales while preserving the "disordered" spatial pattern of infectious cases., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)