{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T23:15:35Z","timestamp":1776122135289,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2022,11,4]],"date-time":"2022-11-04T00:00:00Z","timestamp":1667520000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Institutional Fund Projects","award":["IFPDP-209-22"],"award-info":[{"award-number":["IFPDP-209-22"]}]},{"name":"technical and financial support from the Ministry of Education and Deanship of Scientific Research (DSR), King Abdulaziz University (KAU), Jeddah, Saudi Arabia","award":["IFPDP-209-22"],"award-info":[{"award-number":["IFPDP-209-22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JCM"],"abstract":"<jats:p>Background: Monkeypox virus is gaining attention due to its severity and spread among people. This study sheds light on the modeling and forecasting of new monkeypox cases. Knowledge about the future situation of the virus using a more accurate time series and stochastic models is required for future actions and plans to cope with the challenge. Methods: We conduct a side-by-side comparison of the machine learning approach with the traditional time series model. The multilayer perceptron model (MLP), a machine learning technique, and the Box\u2013Jenkins methodology, also known as the ARIMA model, are used for classical modeling. Both methods are applied to the Monkeypox cumulative data set and compared using different model selection criteria such as root mean square error, mean square error, mean absolute error, and mean absolute percentage error. Results: With a root mean square error of 150.78, the monkeypox series follows the ARIMA (7,1,7) model among the other potential models. Comparatively, we use the multilayer perceptron (MLP) model, which employs the sigmoid activation function and has a different number of hidden neurons in a single hidden layer. The root mean square error of the MLP model, which uses a single input and ten hidden neurons, is 54.40, significantly lower than that of the ARIMA model. The actual confirmed cases versus estimated or fitted plots also demonstrate that the multilayer perceptron model has a better fit for the monkeypox data than the ARIMA model. Conclusions and Recommendation: When it comes to predicting monkeypox, the machine learning method outperforms the traditional time series. A better match can be achieved in future studies by applying the extreme learning machine model (ELM), support vector machine (SVM), and some other methods with various activation functions. It is thus concluded that the selected data provide a real picture of the virus. If the situations remain the same, governments and other stockholders should ensure the follow-up of Standard Operating Procedures (SOPs) among the masses, as the trends will continue rising in the upcoming 10 days. However, governments should take some serious interventions to cope with the virus. Limitation: In the ARIMA models selected for forecasting, we did not incorporate the effect of covariates such as the effect of net migration of monkeypox virus patients, government interventions, etc.<\/jats:p>","DOI":"10.3390\/jcm11216555","type":"journal-article","created":{"date-parts":[[2022,11,8]],"date-time":"2022-11-08T08:52:56Z","timestamp":1667897576000},"page":"6555","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Modeling and Forecasting Monkeypox Cases Using Stochastic Models"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4993-9433","authenticated-orcid":false,"given":"Moiz","family":"Qureshi","sequence":"first","affiliation":[{"name":"Department of Statistics, Shaheed Benazir Bhutto University, Nawabshah 67450, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shahid","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National University of Modern Languages, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rashad A. R.","family":"Bantan","sequence":"additional","affiliation":[{"name":"Department of Marine Geology, Faculty of Marine Science, King AbdulAziz University, Jeddah 21551, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1415-4970","authenticated-orcid":false,"given":"Muhammad","family":"Daniyal","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1333-3862","authenticated-orcid":false,"given":"Mohammed","family":"Elgarhy","sequence":"additional","affiliation":[{"name":"The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra 31951, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9414-4010","authenticated-orcid":false,"given":"Roy Rillera","family":"Marzo","sequence":"additional","affiliation":[{"name":"Department of Community Medicine, International Medical School, Management and Science University, Shah Alam 40100, Selangor, Malaysia"},{"name":"Global Public Health, Jeffrey Cheah School of Medicine and Health Sciences, Monash University Malaysia, Jalan Lagoon Selatan, Subang Jaya 47500, Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4208-9408","authenticated-orcid":false,"given":"Yulan","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Epidemiology and Health Statistics, School of Public Health, Fujian Medical University, Fuzhou 350122, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1128\/br.37.1.1-18.1973","article-title":"Monkeypox virus","volume":"37","author":"Cho","year":"1973","journal-title":"Bacteriol. Rev."},{"key":"ref_2","first-page":"599","article-title":"Isolation and properties of the causal agent of a new variola-like disease (monkeypox) in man","volume":"46","author":"Marennikova","year":"1972","journal-title":"Bull. World Health Organ."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bunge, E.M., Hoet, B., Chen, L., Lienert, F., Weidenthaler, H., Baer, L.R., and Steffen, R. (2022). The changing epidemiology of human monkeypox\u2014A potential threat? A systematic review. PLoS Negl. Trop. Dis., 16.","DOI":"10.1371\/journal.pntd.0010141"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2919","DOI":"10.1128\/JCM.40.8.2919-2921.2002","article-title":"Outbreaks of disease suspected of being due to human monkeypox virus infection in the Democratic Republic of Congo in 2001","volume":"40","author":"Meyer","year":"2002","journal-title":"J. Clin. Microbiol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1093\/oxfordjournals.bmb.a011720","article-title":"Re-emergence of monkeypox in Africa: A review of the past six years","volume":"54","author":"Heymann","year":"1998","journal-title":"Br. Med. Bull."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"102855","DOI":"10.1016\/j.jaut.2022.102855","article-title":"The 2022 outbreak and the pathobiology of the monkeypox virus","volume":"131","author":"Kumar","year":"2022","journal-title":"J. Autoimmun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2200422","DOI":"10.2807\/1560-7917.ES.2022.27.22.2200422","article-title":"Community transmission of monkeypox in the United Kingdom, April to May 2022","volume":"27","author":"Vivancos","year":"2022","journal-title":"Eurosurveillance"},{"key":"ref_8","unstructured":"WHO (2022, July 27). 2022 Monkeypox Outbreak Global Map, Available online: https:\/\/www.cdc.gov\/poxvirus\/monkeypox\/response\/2022\/world-map.html."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wang, Y.-W., Shen, Z.-Z., and Jiang, Y. (2018). Comparison of ARIMA and GM (1, 1) models for prediction of hepatitis B in China. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0201987"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, L., Wang, L., Zheng, Y., Wang, K., Zhang, X., and Zheng, Y. (2017). Time prediction models for echinococcosis based on gray system theory and epidemic dynamics. Int. J. Environ. Res. Public Health, 14.","DOI":"10.3390\/ijerph14030262"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"20180174","DOI":"10.1098\/rsif.2018.0174","article-title":"Evaluation of mechanistic and statistical methods in forecasting influenza-like illness","volume":"15","author":"Kandula","year":"2018","journal-title":"J. R. Soc. Interface"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ren, H., Li, J., Yuan, Z.-A., Hu, J.-Y., Yu, Y., and Lu, Y.-H. (2013). The development of a combined mathematical model to forecast the incidence of hepatitis E in Shanghai, China. BMC Infect. Dis., 13.","DOI":"10.1186\/1471-2334-13-421"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhang, X., Liu, Y., Yang, M., Zhang, T., Young, A.A., and Li, X. (2013). Comparative study of four time series methods in forecasting typhoid fever incidence in China. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0063116"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1111\/j.1365-3156.2006.01630.x","article-title":"Potential of environmental models to predict meningitis epidemics in Africa","volume":"11","author":"Thomson","year":"2006","journal-title":"Trop. Med. Int. Health"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.epidem.2016.12.001","article-title":"Defining epidemics in computer simulation models: How do definitions influence conclusions?","volume":"19","author":"Orbann","year":"2017","journal-title":"Epidemics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.compbiomed.2014.04.007","article-title":"Time-series analysis in the medical domain: A study of Tacrolimus administration and influence on kidney graft function","volume":"50","author":"Kurbalija","year":"2014","journal-title":"Comput. Biol. Med."},{"key":"ref_17","first-page":"348","article-title":"Interrupted time series regression for the evaluation of public health interventions: A tutorial","volume":"46","author":"Bernal","year":"2017","journal-title":"Int. J. Epidemiol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.jclinepi.2018.05.026","article-title":"A methodological framework for model selection in interrupted time series studies","volume":"103","author":"Bernal","year":"2018","journal-title":"J. Clin. Epidemiol."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Polwiang, S. (2020). The time series seasonal patterns of dengue fever and associated weather variables in Bangkok (2003\u20132017). BMC Infect. Dis., 20.","DOI":"10.1186\/s12879-020-4902-6"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1186\/1475-2875-8-61","article-title":"Modelling malaria incidence with environmental dependency in a locality of Sudanese savannah area, Mali","volume":"8","author":"Gaudart","year":"2009","journal-title":"Malar. J."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Wei, W., Jiang, J., Liang, H., Gao, L., Liang, B., Huang, J., Zang, N., Liao, Y., Yu, J., and Lai, J. (2016). Application of a Combined Model with Autoregressive Integrated Moving Average (ARIMA) and Generalized Regression Neural Network (GRNN) in Forecasting Hepatitis Incidence in Heng County, China. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0156768"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zheng, Y.L., Zhang, L.P., Zhang, X.L., Wang, K., and Zheng, Y.J. (2015). Forecast model analysis for the morbidity of tuberculosis in Xinjiang, China. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0116832"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.ijid.2018.07.003","article-title":"Epidemiology and ARIMA model of positive-rate of influenza viruses among children in Wuhan, China: A nine-year retrospective study","volume":"74","author":"He","year":"2018","journal-title":"Int. J. Infect. Dis."},{"key":"ref_24","unstructured":"Roser, M., Ritchie, H., Ortiz-Ospina, E., and Hasell, J. (2020). Coronavirus Pandemic (COVID-19). Our World Data, 4."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Bartholomew, D. (1971). Time Series Analysis Forecasting and Control, Wiley.","DOI":"10.1057\/jors.1971.52"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"764","DOI":"10.15585\/mmwr.mm7123e1","article-title":"Monkeypox outbreak\u2014Nine states, May 2022","volume":"71","author":"Minhaj","year":"2022","journal-title":"Morb. Mortal. Wkly. Rep."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"W-163","DOI":"10.7326\/0003-4819-147-8-200710160-00010-w1","article-title":"Strengthening the Reporting of Observational Studies in Epidemiology (STROBE): Explanation and elaboration","volume":"147","author":"Vandenbroucke","year":"2007","journal-title":"Ann. Intern. Med."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Liu, Q., Liu, X., Jiang, B., and Yang, W. (2011). Forecasting incidence of hemorrhagic fever with renal syndrome in China using ARIMA model. BMC Infect. Dis., 11.","DOI":"10.1186\/1471-2334-11-218"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"105340","DOI":"10.1016\/j.dib.2020.105340","article-title":"Application of the ARIMA model on the COVID-2019 epidemic dataset","volume":"29","author":"Benvenuto","year":"2020","journal-title":"Data Brief."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1177\/002076409904500102","article-title":"Application and Results of the Manchester Short Assessment of Quality of Life (Mansa)","volume":"45","author":"Priebe","year":"1999","journal-title":"Int. J. Soc. Psychiatry"},{"key":"ref_31","unstructured":"Pankratz, A. (2009). Forecasting with Univariate Box-Jenkins Models: Concepts and Cases, John Wiley & Sons."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1093\/biomet\/65.2.297","article-title":"On a measure of lack of fit in time series models","volume":"65","author":"Ljung","year":"1978","journal-title":"Biometrika"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control."}],"container-title":["Journal of Clinical Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2077-0383\/11\/21\/6555\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:10:57Z","timestamp":1760145057000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2077-0383\/11\/21\/6555"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,4]]},"references-count":33,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["jcm11216555"],"URL":"https:\/\/doi.org\/10.3390\/jcm11216555","relation":{},"ISSN":["2077-0383"],"issn-type":[{"value":"2077-0383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,4]]}}}