  The spatial diffusion of epidemic disease follows distance decay law in
geography, but different diffusion processes may be modeled by different
mathematical functions under different spatio-temporal conditions. This paper
is devoted to modeling spatial diffusion patterns of COVID-19 stemming from
Wuhan city to Hubei province. The methods include gravity and spatial
auto-regression analyses. 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 linear regression. 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 observation 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 isolation measures taken by Chinese government against the
transmission of COVID-19 is obvious. This study suggests that the role of
gravity should be taken into account to prevent and control epidemic disease.
