Porcine pasteurellosis outbreak dataAccording to the Ministry of Agriculture and Rural Affairs of the People’s Republic of China, main outbreaks of porcine pasteurellosis in the Chinese mainland were observed in the central and southern China from 2008 to 2020 (http://www.moa.gov.cn/). Sichuan, Chongqing and Guangxi had the most severe outbreaks (Fig. 1a). Between 2008 and 2015, outbreaks of porcine pasteurellosis showed an increasing trend. Since 2015, outbreaks have shown a downward trend (Fig. 1b). Summer (June, July and August) was the main outbreak season for the disease (Fig. 1c).Fig. 1The outbreaks of porcine pasteurellosis in the Chinese mainland from 2008 to 2020. a number of porcine pasteurellosis outbreak in various provinces. b annual number of porcine pasteurellosis outbreak. c monthly number of porcine pasteurellosis outbreak.Study frameworkIn this study, a predictive model for porcine pasteurellosis was developed based on MCDA. According to relevant research, seven spatial risk factors of porcine pasteurellosis were determined7,23. The research framework as shown in Fig. 2 and the specific steps are as follows:
1.
Different influencing factors have different attributes and units, which need to be standardized for all data. The fuzzy membership function was used to complete the standardization of the data with values between 0 and 110.
2.
Principal component analysis (PCA) was used to determine the weight of influencing factors. Since the factors used for evaluation have different spatial resolutions, all factors need to be adjusted to a resolution of 2.5 arcmin (approximately 4.65 km × 4.65 km).
3.
Weighted linear combination (WLC) was used to construct the risk maps of porcine pasteurellosis by combining all risk factors16.
4.
One-At-a-Time (OAT) was used to calculate the uncertainty map, and mean of absolute change rates (MACRs)10.
5.
C# was used as the development language; MCDA was combined with WebGIS technology to construct a system for predicting risk areas of porcine pasteurellosis39.
Fig. 2Study framework to predict risk areas of porcine pasteurellosis based on MCDA.Factors used to risk mapRailway and highwayTransportation plays an important role in spreading animal infectious diseases by increasing the contact rate between sick and healthy animals. The railway and highway data of the Chinese mainland were obtained from Geographic Data Sharing Infrastructure, College of Urban and Environmental Science, Peking University (http://geodata.pku.edu.cn), China. The railway and highway densities in the Chinese mainland were calculated by using kernel density estimation (KDE).Temperature and precipitationTemperature and precipitation are the important factors in the prevalence of porcine pasteurellosis6. The meteorological data were obtained from WorldClim, and the closest data of the current climate conditions were selected24.Pig density and population densityAs the most susceptible animal, pigs play an important role in the development and transmission of the porcine pasteurellosis. Moreover, population density can reflect the main areas of livestock farming and P. multocida is also pathogenic to humans. The population density and pig density data in this study were obtained from WorldPop and the Food and Agriculture Organization of the United Nations (FAO), respectively. The obtained data was resampled and adjusted to be consistent with the extent of the Chinese mainland.Influence degreeResearch on animal infectious diseases based on MCDA needs a leading factor to represent the research object. Therefore, used the number of porcine pasteurellosis outbreaks to reflect the degree of outbreak in various regions. According to previous studies, inverse distance weighting (IDW) is the most suitable method to simulate the impact of porcine pasteurellosis compared with ordinary kriging, local polynomials, and simple kriging25. In this study, we used IDW to interpolate the number of porcine pasteurellosis outbreaks from 2008 to 2020 in various provinces in the Chinese mainland to obtain the influence degree (degree of outbreak) map.Standardization of factorsAfter preprocessing all influencing factors, a raster dataset for the Chinese mainland under the resolution of 2.5 arcmin was obtained. According to studies on other animal infectious diseases, fuzzy membership functions were used to standardize all factors10,15,16. Population density, pig density and the influence degree of porcine pasteurellosis were processed by a linear relationship. Railroad density, highway density, average annual temperature and annual precipitation were standardized by sigmoidal relationship. Finally, seven risk factors were normalized to the spatial maps on a 0–1 scale (Supplement 1).Determining factors weightsMethods in the determination of factor weights include two main categories: subjective assignment and objective assignment. Our study used PCA to determine the weights of each factor. PCA is a kind of recombination of multiple original variables with a strong correlation to generate a few uncorrelated variables and extract information of the original variables. The weight calculation process of the seven factors was as follows:
1.
Calculation of the correlation coefficient matrix:$$R=\left[\begin{array}{cccc} r11 & r12& …& r1p\\ r21& r22& …& r2p\\ …& …& …& …\\ rp1& rp2& …& rpp\end{array}\right]$$
(1)
rij is the correlation coefficient between the original variables xi and xj (i, j = 1, 2, …, p).
2.
Calculation of eigenvalues and eigenvectors.
The characteristic equation is |λE − R| = 0. E is the unit matrix, calculating all the eigenvalues, arranging them in order of magnitude as λ1 ≥ λ2… ≥ λp ≥ 0, and respectively finding the eigenvectors ei(i = 1,2,…,p) corresponding to the eigenvalue λi.
3.
3. Calculation of the cumulative contribution rate of the principal components:$$\frac{\sum_{k=1}^{m}{\lambda }_{k}}{\sum_{k=1}^{p}{\lambda }_{k}}$$
(2)
4.
Calculation of the coefficients of the original index in the linear combination of different principal components (Lij):$${L}_{ij}=\frac{{e}_{ij}}{\sqrt{{\lambda }_{i}}}(i=\text{1,2},…,m; j=\text{1,2},…,p)$$
(3)
eij is the loading of the original index (xj) in the i-th principal component.
5.
Calculation of the contribution rate of the principal components (ui):$${u}_{i}=\frac{{\lambda }_{i}}{{\sum }_{k=1}^{m}{\lambda }_{k}}(i=\text{1,2},…,m)$$
(4)
6.
Calculation of the co`efficient of the original index in the comprehensive model (dj):$${d}_{j}={\sum }_{i=1}^{m}{u}_{i}{L}_{ij}(i=\text{1,2},…,m; j=\text{1,2},…,p)$$
(5)
7.
Normalization of index weight (wj):$${w}_{j}=\frac{{d}_{j}}{{\sum }_{k=1}^{p}{d}_{k}}(j=\text{1,2},…,p)$$
(6)
Construction of risk mapSeven risk factors were weighted using WLC to construct a risk map. The formula is as follows:$$S= {\sum }_{i=1}^{n}{w}_{i}v({a}_{i})$$
(7)
n is the number of risk factors; \(w\) is the weight value of risk factor i; v is the value functions of factors at layer i (ai); and S is the total value of each small grid26. ArcGIS 10.2 (ESRI, Redlands, CA, USA) was used to construct the risk map.Sensitivity analysis and validationOne-At-a-Time is a commonly used sensitivity method, also known as OAT. The purpose of using OAT was to examine the influence of the output factors on the output results27. It reflects the degree and regularity of the influence of a single factor on the result by changing the weight of only one factor at a time. The method has a high comparability and the OAT method is simple and easy to implement.It is necessary to specify a feasible weight deviation range, which can be defined as a range of percent change (RPC) derived from the original standard weight value in basic operations. Various ranges were applied for each criterion, or a single range was used for all criteria. In this study, the RPC was between − 20 and 20%, with a step size of 1%27. The adjusted new weight is calculated using the following formula:$$W({C}_{m},PC)=W({C}_{m},0)+W({C}_{m},0)\times PC (1\le m\le n)$$
(8)
where W(Cm, PC) is the initial weight of the major changing factor Cm, PC is the percentage of weight change, and n is the number of risk factors.$$w({C}_{i},PC)=(1-w({\text{C}}_{\text{m}},\text{PC}))*\frac{{W(C}_{i}, 0)}{1-{\text{w}(\text{C}}_{\text{m}}, 0)} (1\le i\le n,i\ne a)$$
(9)
where W(Ci,0) is the weight of i-th criterion (Ci) at the preliminary weight.Risk factors were compared by calculating the MACRs of the risk map and adjusted-weight map using the following equation:$$\text{MACRs}={\sum }_{k=1}^{N}\left|\frac{{R}_{K}-{R}_{0}}{{R}_{0}}\right|\times 100\%$$
(10)
Where Rk is the adjusted-weight risk map; R0 is the initial risk map; N is the number of pixels.The uncertainty map was the standard deviation of the risk maps generated after all factors changed the weights28,29. Moreover, the outbreak data for porcine pasteurellosis from 2021 to 2022 was used to assess the accuracy of the risk map. The predictive performance of the risk map was evaluated by calculating the receiver operating characteristic (ROC).Construction of prediction systemFigure 3 showed the research framework for WebGIS-based prediction system. C# was used as a development language to develop the system in Microsoft Visual Studio 2012. Model Builder in ArcGIS 10.2 was used to build models, publish and share services dependent on ArcGIS Server. Silverlight and XAML were used to enable the dynamic presentation of simulation features. The data were stored and processed in Oracle 11 g and ArcGIS. Finally, MCDA was combined with WebGIS technology to construct a system for predicting risk areas of porcine pasteurellosis.Fig. 3Study framework for WebGIS-based prediction system. (This map was generated using ArcGIS version 10.2 (Esri, https://www.esri.com/en-us/arcgis/products/arcgis-pro/overview). The base map of China was sourced from the Chinese National Standard Map Service (http://bzdt.ch.mnr.gov.cn/index.html), approval number GS (2020) 4619.)