A kernel-modulated SIR model for Covid-19 contagious spread from county to continent.

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.

COVID-19: A Comparative Study of Population Aggregation Patterns in the Central Urban Area of Tianjin, China.

When a public health emergency occurs, a potential sanitation threat will directly change local residents' behavior patterns, especially in high-density urban areas. Their behavior pattern is typically transformed from demand-oriented to security-oriented. This is directly manifested as a differentiation in the population distribution. This study based on a typical area of high-density urban area in central Tianjin, China. We used Baidu heat map (BHM) data to calculate full-day and daytime/nighttime state population aggregation and employed a geographically weighted regression (GWR) model and Moran's I to analyze pre-epidemic/epidemic population aggregation patterns and pre-epidemic/epidemic population flow features. We found that during the COVID-19 epidemic, the population distribution of the study area tended to be homogenous clearly and the density decreased obviously. Compared with the pre-epidemic period: residents' demand for indoor activities increased (average correlation coefficient of the floor area ratio increased by 40.060%); traffic demand decreased (average correlation coefficient of the distance to a main road decreased by 272%); the intensity of the day-and-night population flow declined significantly (its extreme difference decreased by 53.608%); and the large-living-circle pattern of population distribution transformed to multiple small-living circles. This study identified different space utilization mechanisms during the pre-epidemic and epidemic periods. It conducted the minimum living security state of an epidemic-affected city to maintain the operation of a healthy city in the future.

Population agglomeration is a harbinger of the spatial complexity of COVID-19.

The spatial template over which COVID-19 infections operate is a result of nested societal decisions involving complex political and epidemiological processes at a broad range of spatial scales. It is characterized by 'hotspots' of high infections interspersed within regions where infections are sporadic to absent. In this work, the sparseness of COVID-19 infections and their time variations were analyzed across the US at scales ranging from 10 km (county scale) to 2600 km (continental scale). It was found that COVID-19 cases are multi-scaling with a multifractality kernel that monotonically approached that of the underlying population. The spatial correlation of infections between counties increased rapidly in March 2020; that rise continued but at a slower pace subsequently, trending towards the spatial correlation of the population agglomeration. This shows that the disease had already spread across the USA in early March such that travel restriction thereafter (starting on March 15th 2020) had minor impact on the subsequent spatial propagation of COVID-19. The ramifications of targeted interventions on spatial patterns of new infections were explored using the epidemiological susceptible-infectious-recovered (SIR) model mapped onto the population agglomeration template. These revealed that re-opening rural areas would have a smaller impact on the spread and evolution of the disease than re-opening urban (dense) centers which would disturb the system for months. This study provided a novel way for interpreting the spatial spread of COVID-19, along with a practical approach (multifractals/SIR/spectral slope) that could be employed to capture the variability and intermittency at all scales while maintaining the spatial structure.