{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T23:50:31Z","timestamp":1789084231840,"version":"build-2803163510"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,4]],"date-time":"2017-03-04T00:00:00Z","timestamp":1488585600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11401512"],"award-info":[{"award-number":["11401512"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11461073"],"award-info":[{"award-number":["11461073"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Academic Discipline Project of Xinjiang Medical University-Health Measurements and Health Economics","award":["XYDXK50780308"],"award-info":[{"award-number":["XYDXK50780308"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJERPH"],"abstract":"<jats:p>Echinococcosis, which can seriously harm human health and animal husbandry production, has become an endemic in the Xinjiang Uygur Autonomous Region of China. In order to explore an effective human Echinococcosis forecasting model in Xinjiang, three grey models, namely, the traditional grey GM(1,1) model, the Grey-Periodic Extensional Combinatorial Model (PECGM(1,1)), and the Modified Grey Model using Fourier Series (FGM(1,1)), in addition to a multiplicative seasonal ARIMA(1,0,1)(1,1,0)4 model, are applied in this study for short-term predictions. The accuracy of the different grey models is also investigated. The simulation results show that the FGM(1,1) model has a higher performance ability, not only for model fitting, but also for forecasting. Furthermore, considering the stability and the modeling precision in the long run, a dynamic epidemic prediction model based on the transmission mechanism of Echinococcosis is also established for long-term predictions. Results demonstrate that the dynamic epidemic prediction model is capable of identifying the future tendency. The number of human Echinococcosis cases will increase steadily over the next 25 years, reaching a peak of about 1250 cases, before eventually witnessing a slow decline, until it finally ends.<\/jats:p>","DOI":"10.3390\/ijerph14030262","type":"journal-article","created":{"date-parts":[[2017,3,9]],"date-time":"2017-03-09T06:56:43Z","timestamp":1489042603000},"page":"262","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Time Prediction Models for Echinococcosis Based on Gray System Theory and Epidemic Dynamics"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1508-9066","authenticated-orcid":false,"given":"Liping","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1619-0649","authenticated-orcid":false,"given":"Li","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Public Health, Xinjiang Medical University, Urumqi 830011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanling","family":"Zheng","sequence":"additional","affiliation":[{"name":"College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xueliang","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yujian","family":"Zheng","sequence":"additional","affiliation":[{"name":"College of Public Health, Xinjiang Medical University, Urumqi 830011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.jtbi.2013.04.020","article-title":"Modeling and analysis of the transmission of Echinococcosis with application to Xinjiang Uygur Autonomous Region of China","volume":"333","author":"Wang","year":"2013","journal-title":"J. Theor. Biol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"296","DOI":"10.3201\/eid1202.050499","article-title":"Global socioeconomic impact of cystic Echinococcosis","volume":"12","author":"Budke","year":"2006","journal-title":"Emerg. Infect. Dis."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/S1473-3099(07)70134-2","article-title":"Prevention and control of cystic echinococcosis","volume":"7","author":"Craig","year":"2007","journal-title":"Lancet Infect. Dis."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1128\/CMR.17.1.107-135.2004","article-title":"Biological, epidemiological, and clinical aspects of echinococcosis, a zoonosis of increasing concern","volume":"17","author":"Eckert","year":"2004","journal-title":"Clin. Microbiol. Rev."},{"key":"ref_5","unstructured":"Eckert, J., Gemmell, M.A., Meslin, F.X., and Paw\u0142owski, Z.S. (2001). WHO\/OIE Manual on Echinococcosis in Humans and Animals: A Public Health Problem of Global Concern, World Organisation for Animal Health (Office International des Epizooties) and World Health Organization. [1st ed.]."},{"key":"ref_6","first-page":"125","article-title":"Echinococcosis: A review","volume":"13","author":"Moro","year":"2009","journal-title":"J. Infect. Dis."},{"key":"ref_7","unstructured":"Eckert, J., Gemmell, M.A., Meslin, F.X., and Paw\u0142owski, Z.S. (2001). WHO\/OIE Manual on Echinococcosis in Humans and Animals: A Public Health Problem of Global Concern, World Organisation for Animal Health (Office International des Epizooties) and World Health Organization. [1st ed.]."},{"key":"ref_8","unstructured":"Box, G.E., Jenkins, G.M., Reinsel, G.C., and Ljung, G.M. (2015). Time Series Analysis: Forecasting and Control, John Wiley & Sons, Inc.. [4th ed.]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/S0167-6911(82)80025-X","article-title":"Control problems of grey systems","volume":"1","author":"Deng","year":"1982","journal-title":"Syst. Control Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2767","DOI":"10.1016\/j.eswa.2012.11.002","article-title":"Fifteen years of grey system theory research: A historical review and bibliometric analysis","volume":"40","author":"Yin","year":"2013","journal-title":"Expert Syst. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3816","DOI":"10.1016\/j.apenergy.2011.05.013","article-title":"Grey forecasting model for CO2 emissions: A Taiwan study","volume":"88","author":"Lin","year":"2011","journal-title":"Appl. Energy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1016\/j.ijepes.2012.06.001","article-title":"A proposed grey model for short-term electricity price forecasting in competitive power markets","volume":"43","author":"Lei","year":"2012","journal-title":"Int. J. Electr. Power"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"12946","DOI":"10.1016\/j.eswa.2011.04.091","article-title":"A hybrid approach of HMM and grey model for age-dependent health prediction of engineering assets","volume":"38","author":"Peng","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5387","DOI":"10.1016\/j.eswa.2008.06.103","article-title":"A hybrid model for stock market forecasting and portfolio selection based on ARX, grey system and RS theories","volume":"36","author":"Huang","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Ma, Z., Zhou, Y., and Wu, J. (2009). Modeling and Dynamics of Infectious Diseases, World Scientific Publishing Company. [1st ed.].","DOI":"10.1142\/7223"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4399","DOI":"10.1016\/j.apm.2012.09.052","article-title":"A novel grey forecasting model and its optimization","volume":"37","author":"Cui","year":"2013","journal-title":"Appl. Math. Model."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2241","DOI":"10.1016\/S0196-8904(02)00248-0","article-title":"Applications of improved grey prediction model for power demand forecasting","volume":"44","author":"Hsu","year":"2003","journal-title":"Energy Convers. Manag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9658","DOI":"10.1016\/j.eswa.2008.12.009","article-title":"Adaptive and high-precision grey forecasting model","volume":"36","author":"Lin","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1016\/j.apm.2008.01.011","article-title":"Discrete grey forecasting model and its optimization","volume":"33","author":"Xie","year":"2009","journal-title":"Appl. Math. Model."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6152","DOI":"10.1016\/j.amc.2012.12.015","article-title":"The necessary and sufficient condition for GM(1,1) grey prediction model","volume":"219","author":"Chen","year":"2013","journal-title":"Appl. Math. Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1016\/j.energy.2009.12.021","article-title":"Time series models (Grey-Markov, Grey Model with rolling mechanism and singular spectrum analysis) to forecast energy consumption in India","volume":"35","author":"Kumar","year":"2010","journal-title":"Energy"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.apenergy.2012.01.063","article-title":"Forecasting nonlinear time series of energy consumption using a hybrid dynamic model","volume":"94","author":"Lee","year":"2012","journal-title":"Appl. Energy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3498","DOI":"10.1016\/j.apm.2008.11.012","article-title":"The deterministic grey dynamic model with convolution integral DGDMC(1,n)","volume":"33","author":"Tien","year":"2009","journal-title":"Appl. Math. Model."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/S0040-1625(99)00098-0","article-title":"Applied hybrid grey model to forecast seasonal time series","volume":"67","author":"Tseng","year":"2001","journal-title":"Technol. Forecast. Soc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S0957-4174(01)00047-1","article-title":"Predicting stock price using fuzzy grey prediction system","volume":"22","author":"Wang","year":"2002","journal-title":"Expert Syst. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1016\/j.chaos.2006.05.039","article-title":"An effective hybrid approach based on grey and ARMA for forecasting gyro drift","volume":"35","author":"Zhou","year":"2008","journal-title":"Chaos Soliton Fract."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2759","DOI":"10.1016\/j.energy.2005.02.001","article-title":"Development of an integrated Grey\u2013fuzzy-based electricity management system for enterprises","volume":"30","author":"Yao","year":"2005","journal-title":"Energy"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1784","DOI":"10.1016\/j.eswa.2009.07.064","article-title":"Grey system theory-based models in time series prediction","volume":"37","author":"Kayacan","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1111\/zph.12145","article-title":"Time-series analysis on human brucellosis during 2004\u20132013 in Shandong province, China","volume":"62","author":"Yang","year":"2015","journal-title":"Zoonoses Public Health"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/S1995-7645(12)60095-9","article-title":"Modeling seasonal leptospirosis transmission and its association with rainfall and temperature in Thailand using time-series and ARIMAX analyses","volume":"5","author":"Chadsuthi","year":"2012","journal-title":"Asian Pac. J. Trop. Med."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Wang, T., Liu, J., Zhou, Y., Cui, F., Huang, Z., Wang, L., and Zhai, S. (2016). Prevalence of hemorrhagic fever with renal syndrome in Yiyuan county, China, 2005\u20132014. BMC Infect. Dis., 16.","DOI":"10.1186\/s12879-016-1404-7"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zhang, X., Zhang, T., Pei, J., Liu, Y., Li, X., and Medrano-Gracia, P. (2016). Time series modelling of syphilis in China from 2005 to 2012. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0149401"},{"key":"ref_33","unstructured":"Chinese Bureau of National Statistics (2015). China Statistical Yearbook 2015."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zhang, T., Wang, K., and Zhang, X. (2015). Modeling and analyzing the transmission dynamics of HBV epidemic in Xinjiang, China. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0138765"}],"container-title":["International Journal of Environmental Research and Public Health"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1660-4601\/14\/3\/262\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:29:44Z","timestamp":1760207384000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1660-4601\/14\/3\/262"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,4]]},"references-count":34,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["ijerph14030262"],"URL":"https:\/\/doi.org\/10.3390\/ijerph14030262","relation":{},"ISSN":["1660-4601"],"issn-type":[{"value":"1660-4601","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,4]]}}}