Spatial autocorrelation analysis

The concept of spatial autocorrelation was put forward by Tobler’s first law of geography: spatial autocorrelation refers to the potential interdependence between observed data of some variables in the same distribution area [10]. As a spatial statistical method, global spatial autocorrelation and local spatial autocorrelation are used to describe the relationship between study areas and measure the degree of aggregation or dispersion [11–13]. Moran’s I index is a tool to measure spatial autocorrelation. The global Moran’s I index is used to measures the overall spatial autocorrelation and spatial distribution of the study areas while the local one can be further used to reflects the local spatial autocorrelation and the specific clustering areas [14]. In this study, we used global spatial autocorrelation and local spatial autocorrelation to explore the spatial correlation of bacterial dysentery in Sichuan.

The value of Moran’s I index range from − 1 to + 1. An I > 0 indicates a positive autocorrelation, and the distribution of cases is aggregated in space. An I < 0 indicates a negative autocorrelation and the closer to − 1, the more scattered the cases are. An I = 0 indicates that the cases are randomly distributed in space [15].

The formula for global Moran’s I is:

where n is the number of areas; xi and xj are the observed values of areas i and j; wij is the element in the spatial weight matrix corresponding to the observation pair i,j; The value for wij is 1 if province i and province j are adjacent. Otherwise, the value is 0 [16].

Regardless of the existence of global spatial autocorrelation, the local Moran’s I index can be used to find the hot spots and local autocorrelation that may be concealed [17]. The spatial correlation patterns obtained from the local Moran’s I index can be classified into four types, which are shown by the local indicators of spatial autocorrelation (LISA): low–high cluster (LH, which indicated that the low cluster areas were surrounded by high cluster areas), high–low cluster (HL, which indicated that the high cluster areas were surrounded by other low cluster areas), low–low cluster (LL, which indicated the cold spot), and high–high cluster (HH, which indicated the hot spot) [18, 19].

The formula for local Moran’s I is:I=nS0∑i∑jwijyi-y¯yj-y¯/∑iyi-y¯2

where yi represents the incidence rate in areas i, yj represents the incidence rate in areas j, y¯ indicates the mean value, S0 is the sum of wij [20] We used global Moran’s I and local Moran’s I statistic and LISA map to explore the spatial correlation of BD in Sichuan in ArcGIS 10. 6 software.