Hand, foot and mouth disease: spatiotemporal transmission and climate
© Wang et al; licensee BioMed Central Ltd. 2011
Received: 31 January 2011
Accepted: 5 April 2011
Published: 5 April 2011
The Hand-Foot-Mouth Disease (HFMD) is the most common infectious disease in China, its total incidence being around 500,000 ~1,000,000 cases per year. The composite space-time disease variation is the result of underlining attribute mechanisms that could provide clues about the physiologic and demographic determinants of disease transmission and also guide the appropriate allocation of medical resources to control the disease.
Methods and Findings
HFMD cases were aggregated into 1456 counties and during a period of 11 months. Suspected climate attributes to HFMD were recorded monthly at 674 stations throughout the country and subsequently interpolated within 1456 × 11 cells across space-time (same as the number of HFMD cases) using the Bayesian Maximum Entropy (BME) method while taking into consideration the relevant uncertainty sources. The dimensionalities of the two datasets together with the integrated dataset combining the two previous ones are very high when the topologies of the space-time relationships between cells are taken into account. Using a self-organizing map (SOM) algorithm the dataset dimensionality was effectively reduced into 2 dimensions, while the spatiotemporal attribute structure was maintained. 16 types of spatiotemporal HFMD transmission were identified, and 3-4 high spatial incidence clusters of the HFMD types were found throughout China, which are basically within the scope of the monthly climate (precipitation) types.
HFMD propagates in a composite space-time domain rather than showing a purely spatial and purely temporal variation. There is a clear relationship between HFMD occurrence and climate. HFMD cases are geographically clustered and closely linked to the monthly precipitation types of the region. The occurrence of the former depends on the later.
Hand-Foot-Mouth Disease (HFMD) is the most common gastrointestinal infectious disease in China, mainly among children less than 5 years old, about 91% . HFMD is caused by viruses that belong to the enterovirus genus (group). This group of viruses includes polioviruses, coxsackieviruses, echoviruses, and enteroviruses. The virus transmits through fecal-oral and/or respiratory droplets, or by stool touching, respiratory secretions, herpes solution and polluted staff of patients. The virus can be detected from the stool and pharynx of patients several days before falling ill, the infection reaches the highest point after one week of falling ill, and the stool virus discharges during the last several weeks. Usually the enterovirus exhibits strong transitivity, the latent infection is high and the transmission paths are complicated, causing large epidemics in short times. The disease causes fever, tetter and ulceration on hand, foot and mouth, and may further develop into myocarditis, pulmonary edema, aseptic meningoencephalitis, and other complications [2, 3]. The disease has high infection in China: 488,955 reported cases during the year 2008, with morbidity 37/100,000, mortality 0.0095/100,000 and ill-death rate 0.26/1000, and 1,155,525 cases during 2009.
Many studies have been conducted in recent years seeking to understand the HFMD transmission patterns, and to design evidence-based control strategies. For instance, a significant association between weekly HFMD incidence and 1-2 weeks lagged weekly temperature and rainfall was found in Singapore . From 1979 to November 2010 a total number of 2566 papers indexed by the subject of HFMD were published in Chinese journals. About 80% of the total number of the papers was published during the period 2008-2010, whereas the most intense period of the disease occurred during 2005-2010 . The literature generally focuses on the description and assessment of local outbreaks, incidence and prevalence, demographic distribution among professionals, age, sex, urban/rural, seasons, kindergarten/scattered, clinic characteristics, cure, and responsible virus (EV71, CoxA16). These studies have found that infants and children less than 5 years old are commonly susceptible to the virus (children are more likely to be at risk for infection and illness because they are less likely than adults to have antibodies to protect them; such antibodies develop in the body during a person's first exposure to the enteroviruses that cause HFMD). Although a specific preventive for HFMD is not yet available, the infection risk can be generally lowered by following good hygiene practices. Statistically, the relative risk is expressed by the OR (Odds Ratio) or the RR (Relative Risk), which provides a measure of how many times the relative risk of the exposed group is contained in non-exposed group. The significant disease risk factors are: rural/urban areas (OR = 2.1), drinking behavior (OR = 2.441), infants washing hands before dinner (OR = 0.505) ; float population (OR = 4.507), toy sucking (OR = 3.220) , and low income families . There are certain controversial reports concerning the severity of the disease among kindergarten and scattering children [9, 10]. HFMD is closely correlated with population density and communication . Cities with higher population density and increased float population are at increased risk to the disease, the incidence in the buffer zone between urban and rural being much higher than in both the urban and rural areas . The situation is much more severe in urban than in rural regions, and disease prevalence in plain terrain is higher than in mountainous areas. During May and June, the high disease clustering starts moving from South to North China . The controversial reports on the relative risk of HFMD in rural and urban areas might be due to the different grouping of the buffer zones between rural and urban areas. In many cases the disease symptoms are difficult to be identified by regional health services (doctors etc.), which makes HFMD difficult to control.
Important issues that remain unclear include the spatiotemporal pattern of the HFMD outbreaks in China, and what role climate plays in the transmission of the disease in the space-time domain. As has been reported in the relevant literature, CoxA16 strains are broadly distributed geographically, increased incidence of EV71 infection in young children occurred more often in geographic areas with increased mortality rates , and the genotypes of EV71-associated HFMD differ in space and time [14, 15]. Also, climate indicators can be valuable in the prediction of HFMD activity, which could assist in explaining observed disease peaks across space-time . Answering space-time issues and disease-climate associations can provide valuable information regarding the allocation of public health resources for prevention and treatment purposes [17–19].
Prospective cohort studies could be used, but they are relatively expensive due to the cost of recruiting many individuals who will never be infected, and the high staff cost of the reactive follow-up by medical personnel. A carefully designed prospective cluster study could provide a more efficient way of gathering key data to improve basic understanding of infectious disease transmission dynamics, although substantive problems related to space-time disease change remain unresolved . In fact, most analytical methods used in outbreak detection studies are purely temporal [21–23], which means that these methods can be late at detecting outbreaks that start locally and are linked to serious multiple testing problems generating false signals . Scan statistics methods attempting to resolve such issues are of rather limited usefulness since they make assumptions that are often unrealistic (e.g., a uniform population at risk or ad hoc probability models), or they require information that may be not easily obtainable (e.g., information about the geographical and temporal distribution of populations at risk). Some studies of disease outbreaks (e.g., those based on prospective space-time permutation scan statistics) consider separately purely spatial and purely temporal variations [24, 25], which is a simplification of the natural fact that the disease propagates in a composite space-time domain affected by regional climate dynamics. Significant effort has been made by means of the Kulldorf method to improve the ability to find spatial outbreaks using univariate input. This includes our ongoing study to develop a new method to detect multiple clusters in a study area by constructing two or more clusters in the context of the alternative hypothesis. In fact, many of the above methods have not been designed to account for important associations between disease distribution and meteorological conditions
Given the difficulties of previous statistical studies as regards the handling of the high spatiotemporal data dimensionality and the rigorous representation of composite space-time disease variation, in this work we use the space-time BME-S method, which is a combination of the Bayesian Maximum Entropy (BME) theory and the Self-Organized Map (SOM) technique . The BME-S avoids certain modeling simplifications and dimensionality problems of previous studies and offers a realistic framework for modeling and estimation of the disease distribution in a composite space-time domain. Using readily available and well-tested BME-S software, the present HFMD study provides valuable insight into the disease space-time structure and mechanisms in China and their relation to the meteorological attributes and indicators of the region. Otherwise said, the BME-S methodology considers disease propagation and outbreak detection as interdisciplinary problems, which require the integration of information bases from different fields, e.g., health, environmental and population sciences [27, 28].
Methods and Data
where fX;kis probability density function (pdf) of the attribute X p at each space-time point p k ; A is a normalization parameter; g G is a vector with elements representing the G-KB; μ G is a space-time vector with elements that assign proper weights to the elements of g G and are the solutions of the system of equations and ξ S represents the S-KB available. Unlike previous statistical studies of HFMD, the BME theory can incorporate core knowledge G in terms of epidemic laws, when available, in addition to site-specific information S in terms of case numbers.
at each point p k in the space-time domain of interest.
We studied the relationship between the observable disease variation in the space-time population domain and the underlying transmission mechanisms on the basis of the HFMD data available. SOM techniques were used to reduce the high dimensionality of the spatiotemporal HFMD cases into a two dimensional map that discloses disease dynamics at the country level and to explore the underlining demographic and physiologic determinants. In order to investigate the commonly suspicious role of climatology, the station-based climate observations are interpolated across space-time by means of the BME theory. In this way the climate observations are matched to the county-based disease data, and the high dimensionality of the spatiotemporal climate data is also mapped onto the two dimensional framework as the disease using the SOM technique. The method resulting from the integration of BME and SOM is termed BME-S . The subsequent comparison of the BME-S maps of disease distribution and climate variation unveils important disease-climate associations.
every effort has been made to filter out X and e. In this study, HFMD incidence and climate are set as X separately. The BME-S method is used as Θ because it can filter out spatiotemporal regularity (Y) of X by retaining spatial topology in clustering; BME-S is robust to extreme values by normalization of input.
A dataset is classified by SOM into a number of categories according to data similarities. Although similarities could be detected either in the magnitude or in the structure of two vectors, the later is the focus of the present HFMD study. In order to study (a) the overall spatiotemporal indicator similarity, (b) the temporal similarity of spatial patterns, and (c) the spatial similarity of temporal patterns, we need to remove the magnitude differences between all 1456 × 11 spatiotemporal cells, between the 11 time slices, and between the 1456 counties, respectively. Both the HFMD incidence and the climate indicators are re-scaled within the 0-1 range.
Three kinds of normalizations were conducted: (i) global normalization in which all values were normalized into the 0-1 range based on all 1456 × 11 spatiotemporal cells; (ii) time normalization in which all values were normalized into the 0-1 range among the 1456 counties for each of the 11 time slices, so that the between months' difference of the HFMD magnitude is removed and the similarity of the spatial pattern between months is focused; (iii) cell normalization in which all values were normalized within the 0-1 range among all 11 months for each of the 1456 counties, so that the between counties' differences of the HFMD incidence or a climate indicator are reduced and the focus is the similarity of temporal patterns between counties.
Normalization removes the attribute magnitude effect to allow the comparison between spatiotemporal, spatial, and temporal structures. It would be helpful to keep in mind that the spatiotemporal type is a second order characteristic, i.e., the spatiotemporal structure of a quantity rather than the quantity itself.
Results and Interpretation
Figure 4 shows that the planes related to temperatures including average temperature (Ave_temp), average maximum temperature (Ave_max_temp), average minimum temperature (Ave_min_temp), extreme maximum temperature (Ext_man_temp) and extreme minimum temperature (Ext_min_temp) are very similar, in which case we used TEMP to generally denote the temperature-related quantities in the present study. Temperature differences (Dif_temp) and sunshine hours (Sun) are somewhat similar, but are negatively correlated to the average humidity (Ave_hum) and rainfall (Rain). The HFMD incidence SOM (Case_rate) is to some extent correlated to TEMP SOM, and is quite similar to the Rain SOM, which means that the spatiotemporal transmission of HFMD is closely related to the spatiotemporal pattern of rainfall or its confounding factor(s). Below we will discuss the association in more detail.
HFMD Spatiotemporal Types
To readily understand and interpret the spatiotemporal type, below we start with the precipitation Figure 5(2, 4, 6) using existing knowledge on climate; then, we proceed with the disease Figure 5(1, 3, 5); and finally Figure 5(1, 3, 5) are compared with Figure 5(2, 4, 6). More specifically, Figure 5(2, 4, 6) show that the spatiotemporal precipitation types are spatially compact, i.e., the precipitation pattern is continuous across space-time. However, this is not the case with HFMD incidence, Figure 5(1, 3, 5), where the corresponding spatiotemporal types are much less spatially continuous. Figure 5(2) shows greater similarity to Figure 5(4) than to Figure 5(6), which means that the global spatiotemporal types Figure 5(2) are controlled mainly by the similarity of spatial patterns rather than by the similarity of temporal series. At a global level, there is an obvious northeast to southwest belt in Figure 5(6), which is completely consistent with the country's large scale geomorphic and the southeast seasonal wind (both have maximum variation along the northwest-southeast direction). Within the southeast seasonal wind domain, Figure 5(4) shows a greater variability than Figure 5(6), because the spatial precipitation pattern (Figure 5(4)) is more influenced by the local geomorphic than by the monthly precipitation series (Figure 5(6)). There is a big tongue extending into the country along the Yangtze river basin in Figure 5(2), which reflects the spatial similarity of the spatiotemporal precipitation structure in the region.
Just as is the case with the similarity of Figure 5(2, 4), the overall HFMD spatiotemporal type Figure 5(1) is controlled mainly by the spatial disease pattern (Figure 5(3)) rather than by the temporal pattern (Figure 5(5)). Unlike the monthly precipitation Figure 5(2, 4, 6), the Figure 5(1, 3, 5) of the HFMD spatiotemporal types are highly varied throughout the country and less spatially continuous (i.e., characterized more by local outbreaks). There are four clear spatial clusters of high HFMD incidence: Yangtze delta, Middle china, Peal delta and the neighbor to Vietnam in Figure 5(1, 3). The clusters are marked by circles and seem to be spatially consistent with the precipitation spatiotemporal clusters in Figure 5(2, 4). The above clearly imply that the HFMD outbreaks are affected by the spatiotemporal types of monthly precipitation. Besides spatial clusters, the Figure 5(1, 3, 5) illustrates the existence of first case occurrences across the country, i.e. HFMD cases occurring in villages, communities, kindergartens, schools or counties that are epidemiologically independent in space and time (this sporadic feature cannot be explained in terms of climate).
The peak time varies among the different regions of the country. HFMD incidence is relative high in many parts of the country during May-July 2008. Peak periods in regions with higher precipitation levels also occurred during May-August, and then during May 2008 (this is clearly shown in Figure 6), which verified the existence of a certain incidence-precipitation association.
Conclusion and Discussion
The present study investigated composite space-time distribution of HFMD cases and their relationship with regional climate indicators. The spatiotemporal datasets with different formats were matched by the BME theory, and the high dimensionality datasets (in which the spatial and temporal topology was retained) were reduced and mapped onto two-dimensional maps. 16 spatiotemporal types of HFMD cases and climate indicators were identified in these maps, and an association between them was detected.
Besides the significant association between HFMD spatiotemporal type and monthly precipitation spatiotemporal type, we also applied data exploratory analysis and the BME-S method to other climate indicators and we found the next to the significant factors. The pressure distribution during the 11 months (maps not shown here) was relatively stable in most regions. During May-August 2008 the pressure was a little low, then it rapidly rose until its maximum in January 2009; after that the pressure began declining, which was the opposite behavior from that of the incidence distribution. Temperature variation (maps not shown here) was the opposite behavior from that of pressure variation, and seems to suggest a certain similarity between temperature and HFMD variation.
The association between the HFMD spatiotemporal clusters and the spatiotemporal types of monthly precipitation makes it possible to forecast the risk of a disease outbreak on the basis of the prediction of spatiotemporal precipitation types (obtained by means of atmospheric science methods). Intervention and prevention measures should focus predominantly on kindergartens and junior schools located in the HFMD risk areas during the risk periods estimated by the physical methods of atmospheric science and meteorological forecasting.
Compared to similar studies on HFMD (i.e. demographic distribution among professionals, age, sex, urban/rural, seasons, kindergarten/scattered, clinic characteristics, cure, virus and time series association between HFMD and climate), this study identified the spatiotemporal types of HFMD, and its association with precipitation in a large territory. An advantage of the study is that it takes advantage of the fact that we adopt the recently proposed methodology (BME-S) to analyze efficiently the relatively large volume of multi-dimensional data, where the complexity stems from processing several indicators and the disease data in the three-dimensional space-time continuum. Essentially, BME-S is a combination of the BME technique for geostatistical space-time prediction of the indicators' values at unsampled locations in the study area, and of the SOM technique to handle and map efficiently multi-dimensional information. BME does not suffer certain well-known drawbacks of mainstream statistical estimation techniques such as Kriging : like other methods of the statistical regression type , Kriging is restricted to the first-and second-order spatial moments of the attribute, it is a linear interpolator that relies on the Gaussian assumption , and it uses mainly hard (i.e., exact) or hardened data available at a set of neighboring points . SOM creates a topologically ordered partition in a visible two-dimensional plane. In other words, the first cluster is near to the second cluster but away from the ninth cluster. The relationship among the clusters is indicated by means of the order and is clearly displayed on the plane. The topology of the SOM helps it outperform mature methods such as hierarchical, k-means [42, 46]. There are two criteria to evaluate the created SOM: the first one is data representation accuracy, and the other one is the accuracy of the dataset topology considered.
The limitation of the study is that we used 11 months' data (rather than data from the whole year), due to data accessibility issue. The current conclusion is based on monthly data, whereas more accurate findings would have emerged if weekly or daily data were used. HFMD is associated to climate through the interaction between enterovirus activity and human exposure, which both increase during climate change. The biological relationship between climate indicators and enterovius activity is quite complicated, and a mathematical modelling of HFMD spatiotemporal transmission over large territory would display scenarios under different climate conditions. All the above cases deserve to be investigated in future studies.
The space-time BME and SOM software used in this paper is available, free of charge, via the websites http://homepage.ntu.edu.tw/~hlyu/software/SEKSGUI/SEKSHome.html, with paper , and http://www.cis.hut.fi/somtoolbox/download/, with paper [42, 48].
This study was supported by MOST China (2009ZX10004-201, 2008BA156B02, 2006BAK01A13), NSFC (41023010), and CAS China (XDA05090102, KZCX2-YW-308).
- China CDC: 2009,http://www.cdcp.org.cn/editor/uploadfile/20090429174659788.ppthttp://www.cdcp.org.cn/editor/uploadfile/20090429174659788.ppt
- Lum LC, Wong KT, Lam SK, Chua KB, Goh AY, Lim WL, Ong BB, Paul G, AbuBakar S, Lambert M: Fatal enterovirus 71 encephalomyelitis. J Pediatr. 1998, 133 (6): 795-8.View ArticlePubMedGoogle Scholar
- Li LJ: Review of hand, foot and mouth disease. Frontiers of Medicine in China. 2010, 4 (2): 139-146.View ArticleGoogle Scholar
- Hii YL, Rocklov J, Ng N: Short term effects of weather on Hand, Foot and Mouth Disease. PLoS ONE. 2011, 6 (2): e16796-PubMed CentralView ArticlePubMedGoogle Scholar
- Yao XJ, Hao C, Xu H, Chen C, Zhang HL, Deng YM: Investigation of the risk factors of hand-foot-mouth disease in Changzhou. Acta Universitatis Medicinalis Nanjing (Natural Science). 2010, 30 (9): 1275-1278.Google Scholar
- Li ST: Analysis of HFMD epidemiology and risk factors in Hebei district of Tianjin from 2008 to 2009. Port Health Control. 2010, 15 (4): 26-28.Google Scholar
- Cao MH, Liu H, Wan JF, Zhu LY: An case-control study of severe case of hand-foot-and-mouth disease (EV71) in Fuyang City, Anhui Province. Anhui Journal of Preventive Medicine. 2010, 16 (1): 19-20.Google Scholar
- Liang XF, Huang HM, Xie M, Zhang JQ, Hu J: Epidemiological analysis of hand-foot-mouth disease in Shanghai Yangpu District during 2005-2008. Chinese Journal of Disease Control & Prevention. 2010, 14 (6): 512-515.Google Scholar
- Chen HM, Kang K, Wang HF, Wang YX, Su J: Analysis of HFMD s epidemic situation of 2009 in Henan province, forecast of HFMD prevalence trend, prevention and control strategy of 2010. Henan Journal of Preventive Medicine. 2010, 21 (3): 161-169.Google Scholar
- Cao ZD, Zeng DJ, Wang QY, Zheng XL, Wang FY: An epidemiological analysis of the Beijing 2008 Hand-Foot-Mouth epidemic. Chinese Science Bulletin. 2010, 55 (12): 1142-1149.View ArticleGoogle Scholar
- Bie QQ, Qiu DS, Hu H, Ju B: Spatial and temporal distribution characteristics of hand-foot-mouth disease in China. Journal of Geo-Information Science. 2010, 12 (3): 380-384.View ArticleGoogle Scholar
- Chang LY, King CC, Hsu KH, Ning HC, Tsao KC, Li CC, Huang YC, Shih SR, Chiou ST, Chen PY, Chang HJ, Lin TY: Risk factors of enterovirus 71 infection and associated hand, foot, and mouth disease/herpangina in children during an epidemic in Taiwan. Pediatrics. 2002, 109 (6): e88-View ArticlePubMedGoogle Scholar
- Zhang Y, Tan XJ, Wang HY: An outbreak of hand, foot, and mouth disease associated with subgenotype C4 of human enterovirus 71 in Shandong, China. J Clin Virol. 2009, 262-267. 44Google Scholar
- Zhu Z, Abernathy E, Cui A, Zhang Y, Zhou S, Zhang Z, Wang C, Wang T, Ling H: Rubella Virus Genotypes in the People's Republic of China between 1979 and 2007: a Shift in Endemic Viruses during the 2001 Rubella Epidemic. J Clin Microbiol. 2010, 48: 1775-1781.PubMed CentralView ArticlePubMedGoogle Scholar
- Ma E, Lam T, Wong C, Chuang SK: Is hand, foot and mouth disease associated with meteorological parameters. Epidemiology and Infection. 2010, 138 (12): 1779-88.View ArticlePubMedGoogle Scholar
- Chen CC, Wu KY, Chang MJW: A statistical assessment on the stochastic relationship between biomarker concentrations and environmental exposures. Stochastic Environmental Research and Risk Assessment. 2004, 18: 377-385.View ArticleGoogle Scholar
- Hay SI, Snow RW: The malaria atlas project: developing global maps of malaria risk. PLoS Med. 2006, 3 (12): e473-PubMed CentralView ArticlePubMedGoogle Scholar
- Tamerius JD, Wise EK, Uejio CK, McCoy AL, Comrie AC: Climate and human health: synthesizing environmental complexity and uncertainty. Stochastic Environmental Research and Risk Assessment. 2007, 21: 601-613.View ArticleGoogle Scholar
- Riley S: A prospective study of spatial clusters gives valuable insights into dengue transmission. PLoS Med. 2008, 5 (11): e220-PubMed CentralView ArticlePubMedGoogle Scholar
- Nobre FF, Stroup DF: A monitoring system to detect changes in public health surveillance data. Int J Epidemiol. 1994, 23: 408-418.View ArticlePubMedGoogle Scholar
- Hutwagner LC, Maloney EK, Bean NH, Slutsker L, Martin SM: Using laboratory-based surveillance data for prevention: an algorithm for detecting salmonella outbreaks. Emerg Infect Dis. 1997, 3: 395-400.PubMed CentralView ArticlePubMedGoogle Scholar
- Reis B, Mandl K: Time series modeling for syndromic surveillance. BMC Med Inform Decis Mak. 2003, 3: 2-PubMed CentralView ArticlePubMedGoogle Scholar
- Kulldorff M, Heffernan H, Hartman J, Assuncao R, Mostashari F: A space-time permutation scan statistic for disease outbreak detection. PLoS Medicine. 2005, 2 (3): 0216-0224.View ArticleGoogle Scholar
- Mostashari F, Kulldorff M, Hartman JJ, Miller JR, Kulasekera V: Dead bird clustering: A potential early warning system for West Nile virus activity. Emerg Infect Dis. 2003, 9: 641-646.PubMed CentralView ArticlePubMedGoogle Scholar
- Kolovos A, Eskupin A, Jerrett M, Christakos G: Multi-perspective analysis and spatiotemporal mapping of air pollution monitoring data. Environ Sci Technol. 2010, 44: 6738-6744.View ArticlePubMedGoogle Scholar
- Christakos G, Olea RA, Serre ML, Yu HL, Wang LL: Interdisciplinary Public Health Reasoning and Epidemic Modelling: The Case of Black Death. 2005, Springer-Verlag: New York, NYGoogle Scholar
- Christakos G: Integrative Problem-Solving in a Time of Decadence. 2010, Springer-Verlag, New York, NYGoogle Scholar
- Christakos G: Modern Spatiotemporal Geostatistics. 2000, Oxford University Press: OxfordGoogle Scholar
- Christakos G, Bogaert P, Serre ML: Temporal GIS. 2002, Springer-Verlag: New York, NYGoogle Scholar
- Wibrin MA, Bogaert P, Fasbender D: Combining categorical and continuous spatial information within the Bayesian Maximum Entropy paradigm. Stochastic Environmental Research and Risk Assessment. 2006, 20: 423-434.View ArticleGoogle Scholar
- Choi KM, Yu HL, Wilson ML: Spatiotemporal statistical analysis of influenza mortality risk in the State of California during the period 1997-2001. Stochastic Environmental Research and Risk Assessment. 2008, 22 (1): 15-25.View ArticleGoogle Scholar
- Bogaert P: Spatial prediction of categorical variables: the BME approach. Stochastic Environmental Research and Risk Assessment. 2002, 18: 425-448.View ArticleGoogle Scholar
- Yu HL, Kolovos A, Christakos G, Chen JC, Warmerdam S, Dev B: Interactive spatiotemporal modelling of health systems: the SEKS-GUI framework. Stochastic Environmental Research and Risk Assessment. 2007, 21 (5): 555-572.View ArticleGoogle Scholar
- Saito H, McKenna SA, Zimmerman DA, Coburn TC: Geostatistical interpolation of object counts collected from multiple strip transects: Ordinary Kriging versus finite domain Kriging. Stochastic Environmental Research and Risk Assessment. 2005, 19 (1): 71-85.View ArticleGoogle Scholar
- Kumar U, Jain VK: ARIMA forecasting of ambient air pollutants (O3, NO, NO2 and CO). Stochastic Environmental Research and Risk Assessment. 2010, 24 (5): 751-760.View ArticleGoogle Scholar
- Orton TG, Lark RM: Accounting for the uncertainty in the local mean in spatial prediction by BME. Stochastic Environmental Research and Risk Assessment. 2007, 21 (6): 773-784.View ArticleGoogle Scholar
- Kohonen T: Self-organized information of topologically correct features maps. Biological Cybernetics. 1982, 43: 59-69.View ArticleGoogle Scholar
- Li CH, Li N, Shi PJ: The principle and application of self-organizing mapping network in the cluster of cultivated land use pressure in China. Journal of Beijing Normal University (Natural Science). 2006, 42 (5): 543-547.Google Scholar
- Liu YG, Weisberg RH: Patterns of ocean current variability on the West Florida Shelf using the self-organizing map. Journal of Geophysics Research. 2005, 110: C06003-Google Scholar
- Mo LP: A method for fault diagnosis based on kohonen neural network. Journal of Chengdu University (Natural Science edition). 2007, 26 (1): 48-51.Google Scholar
- Vesanto J, Himberg J, Alhonieni E, Parhankangas J: SOM Toolbox for Matlab. 2000Google Scholar
- Olea RA: Geostatistics for Engineers and Earth Scientists. 1999, Kluwer Acad. Publ., Boston, MAView ArticleGoogle Scholar
- Harris P, Brunsdon C, Fotheringham AS: Links, comparisons and extensions of the geographically weighted regression model when used as a spatial predictor. Stochastic Environmental Research and Risk Assessment. 2011, 25: 123-138.View ArticleGoogle Scholar
- Emery X: Multigaussian kriging for point-support estimation: incorporating constraints on the sum of the kriging weights. Stochastic Environmental Research and Risk Assessment. 2006, 20 (1-2): 53-65.View ArticleGoogle Scholar
- Bayraktar H, Turalioglu FS: A Kriging-based approach for locating a sampling site in the assessment of air quality. Stochastic Environmental Research and Risk Assessment. 2005, 19 (4): 301-305.View ArticleGoogle Scholar
- Kolovos A, Yu HL, Christakos G: SEKS-GUI v.0.6 User Manual. 2006, Dept. of Geography, San Diego State University, San Diego, CAGoogle Scholar
- Skupin A, Hagelman R: Visualizing demographic trajectories with self-organizing maps. GeoInformatica. 2005, 9 (2): 159-179.View ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.