Data analysis

We first used Global Moran’s I to initially evaluate spatial clustering of each disease. Moran’s I is a measure of spatial autocorrelation which is characterized by a correlation in a signal among nearby locations in space. If significant spatial autocorrelation was found, we then used local indicators of spatial autocorrelation (LISA) to evaluate the location of disease clusters. Second, we used multilevel negative binomial regression model or zero-inflated negative binomial regression (for disease with an extensive number of zero values) using the Bayesian framework to analyse the association between socio-ecological factors and variation of each communicable disease. The spatial autoregressive models comprising spatial lags, which were a weighted average of observations on the diseases over neighbouring units, were input into the model to adjust for spatial variation of the disease outcomes. Modelled values of temperatures and humidity were centred on the mean values for each variable. The seasonal effect was controlled by dummy variables of the month of a year, and the population was controlled using its offset variable. The general model is described in Eq 1.

where, y_i denotes the monthly counts of Disease d in Province i at month t; ∑j=1nwijyj is a spatial lag, and the w_ij are the spatial weights; S_n is socio-economic factors: all variables were included at one time in Eq 1; T_t is the monthly temperature on month t; H_t is the monthly humidity; and R_t is monthly cumulative rainfall; M_t is the dummy variable of month t; and ε_i is a random intercept.

We conducted an initial burn-in of 2,500 iterations that were default subsequently discarded, and a subsequent set of 10,000 iterations was conducted for the model. The convergence was assessed by visual inspection of posterior density plots, history plots, and autocorrelation of selected parameters. Non-informative N(0,1000) priors were used for all means and Gamma(1,1) priors for variances [33]. Sensitivity analyses with maximum and minimum temperature as instead of average temperatures were also conducted using the same procedures, in which we also used the same non-informative priors for the minimum and maximum temperatures. We used the package “Bayes:” developed for Stata software version 15.0 to analyse data using the Bayesian framework (StataCorp. 2017. Bayesian Analysis Reference Manual Release 15. College Station, TX: Stata Press).