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The spatial diffusion of epidemic disease follows distance decay law in geography and social physics, but the mathematical models of distance decay depend on concrete spatio-temporal conditions. This paper is devoted to modeling spatial diffusion patterns of COVID-19 stemming from Wuhan city to Hubei province, China. The modeling approach is to integrate analytical method and experimental method. The local gravity model is derived from allometric scaling and global gravity model, and then the parameters of the local gravity model are estimated by observational data and least squares calculation. The main results are as below. The local gravity model based on power law decay can effectively describe the diffusion patterns and process of COVID-19 in Hubei Province, and the goodness of fit of the gravity model based on negative exponential decay to the observational data is not satisfactory. Further, the goodness of fit of the model to data entirely became better and better over time, the size elasticity coefficient increases first and then decreases, and the distance attenuation exponent decreases first and then increases. Moreover, the significance of spatial autoregressive coefficient in the model is low, and the confidence level is less than 80%. The conclusions can be reached as follows. (1) The spatial diffusion of COVID-19 of Hubei bears long range effect, and the size of a city and the distance of the city to Wuhan affect the total number of confirmed cases. (2) Wuhan direct transmission is the main process in the spatial diffusion of COVID-19 in Hubei at the early stage, and the horizontal transmission between regions is not significant. (3) The effect of spatial lockdown and isolation measures taken by Chinese government against the transmission of COVID-19 is obvious. This study suggests that the role of urban gravity (size and distance) should be taken into account to prevent and control epidemic disease. [ABSTRACT FROM AUTHOR]

Fractal dimension curves of urban growth can be modeled with sigmoid functions, including logistic function and quadratic logistic function. Different types of logistic functions indicate different spatial dynamics. The fractal dimension curves of urban growth in Western countries follow the common logistic function, while the fractal dimension growth curves of cities in northern China follow the quadratic logistic function. Now, we want to investigate whether other Chinese cities, especially cities in South China, follow the same rules of urban evolution and attempt to analyze the reasons. This paper is devoted to exploring the fractals and fractal dimension properties of the city of Shenzhen in southern China. The urban region is divided into four subareas using ArcGIS technology, the box-counting method is adopted to extract spatial datasets, and the least squares regression method is employed to estimate fractal parameters. The results show that (1) the urban form of Shenzhen city has a clear fractal structure, but fractal dimension values of different subareas are different; (2) the fractal dimension growth curves of all the four study areas can only be modeled by the common logistic function, and the goodness of fit increases over time; (3) the peak of urban growth in Shenzhen had passed before 1986 and the fractal dimension growth is approaching its maximum capacity. It can be concluded that the urban form of Shenzhen bears characteristics of multifractals and the fractal structure has been becoming better, gradually, through self-organization, but its land resources are reaching the limits of growth. The fractal dimension curves of Shenzhen's urban growth are similar to those of European and American cities but differ from those of cities in northern China. This suggests that there are subtle different dynamic mechanisms of city development between northern and southern China. [ABSTRACT FROM AUTHOR]