{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T17:24:36Z","timestamp":1770225876904,"version":"3.49.0"},"reference-count":65,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,4]],"date-time":"2022-07-04T00:00:00Z","timestamp":1656892800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>On 31 December 2019, a cluster of pneumonia cases of unknown etiology was reported in Wuhan (China). The cases were declared to be Coronavirus Disease 2019 (COVID-19) by the World Health Organization (WHO). COVID-19 has been defined as SARS Coronavirus 2 (SARS-CoV-2). Some countries, e.g., Italy, France, and the United Kingdom (UK), have been subjected to frequent restrictions for preventing the spread of infection, contrary to other ones, e.g., the United States of America (USA) and Sweden. The restrictions afflicted the evolution of trends with several perturbations that destabilized its normal evolution. Globally, Rt has been used to estimate time-varying reproduction numbers during epidemics. Methods: This paper presents a solution based on Deep Learning (DL) for the analysis and forecasting of epidemic trends in new positive cases of SARS-CoV-2 (COVID-19). It combined a neural network (NN) and an Rt estimation by adjusting the data produced by the output layer of the NN on the related Rt estimation. Results: Tests were performed on datasets related to the following countries: Italy, the USA, France, the UK, and Sweden. Positive case registration was retrieved between 24 February 2020 and 11 January 2022. Tests performed on the Italian dataset showed that our solution reduced the Mean Absolute Percentage Error (MAPE) by 28.44%, 39.36%, 22.96%, 17.93%, 28.10%, and 24.50% compared to other ones with the same configuration but that were based on the LSTM, GRU, RNN, ARIMA (1,0,3), and ARIMA (7,2,4) models, or an NN without applying the Rt as a corrective index. It also reduced MAPE by 17.93%, the Mean Absolute Error (MAE) by 34.37%, and the Root Mean Square Error (RMSE) by 43.76% compared to the same model without the adjustment performed by the Rt. Furthermore, it allowed an average MAPE reduction of 5.37%, 63.10%, 17.84%, and 14.91% on the datasets related to the USA, France, the UK, and Sweden, respectively.<\/jats:p>","DOI":"10.3390\/e24070929","type":"journal-article","created":{"date-parts":[[2022,7,4]],"date-time":"2022-07-04T11:15:05Z","timestamp":1656933305000},"page":"929","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Forecasting COVID-19 Epidemic Trends by Combining a Neural Network with Rt Estimation"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2237-6984","authenticated-orcid":false,"given":"Pietro","family":"Cinaglia","sequence":"first","affiliation":[{"name":"Department of Health Sciences, Magna Graecia University of Catanzaro, 88100 Catanzaro, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1502-2387","authenticated-orcid":false,"given":"Mario","family":"Cannataro","sequence":"additional","affiliation":[{"name":"Department of Medical and Surgical Sciences, Magna Graecia University of Catanzaro, 88100 Catanzaro, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.ijid.2020.01.050","article-title":"Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak","volume":"92","author":"Zhao","year":"2020","journal-title":"Int. J. Infect. Dis."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.ijid.2015.10.024","article-title":"Bridging the gap between evidence and policy for infectious diseases: How models can aid public health decision-making","volume":"42","author":"Knight","year":"2016","journal-title":"Int. J. Infect. Dis."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.cca.2020.05.044","article-title":"COVID-19: Transmission, prevention, and potential therapeutic opportunities","volume":"508","author":"Lotfi","year":"2020","journal-title":"Clin. Chim. Acta"},{"key":"ref_4","first-page":"33","article-title":"Contributions to the mathematical theory of epidemics\u2013I. 1927","volume":"53","author":"Kermack","year":"1991","journal-title":"Bull. Math. Biol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"e19115","DOI":"10.2196\/19115","article-title":"Prediction of the COVID-19 Pandemic for the Top 15 Affected Countries: Advanced Autoregressive Integrated Moving Average (ARIMA) Model","volume":"6","author":"Singh","year":"2020","journal-title":"JMIR Public Health Surveill."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"a025452","DOI":"10.1101\/cshperspect.a025452","article-title":"Biology of Malaria Transmission","volume":"7","author":"Meibalan","year":"2017","journal-title":"Cold Spring Harb. Perspect. Med."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"145","DOI":"10.3934\/mbe.2008.5.145","article-title":"Mathematical analysis of the transmission dynamics of HIV\/TB coinfection in the presence of treatment","volume":"5","author":"Sharomi","year":"2008","journal-title":"Math. Biosci. Eng."},{"key":"ref_8","first-page":"4","article-title":"Time Series Forecasting of US COVID-19 Transmission","volume":"27","author":"Ding","year":"2021","journal-title":"Altern. Ther. Health Med."},{"key":"ref_9","first-page":"87","article-title":"Epidemiology of Coronavirus disease outbreak: The Italian trends","volume":"15","author":"Abenavoli","year":"2020","journal-title":"Rev. Recent Clin. Trials"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"309","DOI":"10.2174\/1574887116666210401124945","article-title":"SARS-CoV-2 spread dynamics in Italy: The Calabria experience","volume":"16","author":"Abenavoli","year":"2021","journal-title":"Rev. Recent Clin. Trials"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1111\/j.1553-2712.1998.tb02493.x","article-title":"Statistical methodology: V. Time series analysis using autoregressive integrated moving average (ARIMA) models","volume":"5","author":"Nelson","year":"1998","journal-title":"Acad. Emerg. Med."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sadia, F., Boyd, S., and Keith, J.M. (2018). Bayesian change-point modeling with segmented ARMA model. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0208927"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"110212","DOI":"10.1016\/j.chaos.2020.110212","article-title":"Predictions for COVID-19 with deep learning models of LSTM, GRU and Bi-LSTM","volume":"140","author":"Shahid","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1590\/S0037-86822012000100031","article-title":"SARIMA for predicting the cases numbers of dengue","volume":"45","author":"Wiwanitkit","year":"2012","journal-title":"Rev. Soc. Bras. Med. Trop."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Li, Z., and Li, Y. (2020). A comparative study on the prediction of the BP artificial neural network model and the ARIMA model in the incidence of AIDS. BMC Med. Inf. Decis. Mak., 20.","DOI":"10.1186\/s12911-020-01157-3"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1007\/s42979-020-00298-6","article-title":"COVID-19 Pandemic: ARIMA and Regression Model-Based Worldwide Death Cases Predictions","volume":"1","author":"Chaurasia","year":"2020","journal-title":"SN Comput. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Qi, C., Zhang, D., Zhu, Y., Liu, L., Li, C., Wang, Z., and Li, X. (2020). SARFIMA model prediction for infectious diseases: Application to hemorrhagic fever with renal syndrome and comparing with SARIMA. BMC Med. Res. Methodol., 20.","DOI":"10.1186\/s12874-020-01130-8"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1136\/ip.2006.014027","article-title":"Raised speed limits, case fatality and road deaths: A six year follow-up using ARIMA models","volume":"13","author":"Friedman","year":"2007","journal-title":"Inj. Prev."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"104509","DOI":"10.1016\/j.rinp.2021.104509","article-title":"On the accuracy of ARIMA based prediction of COVID-19 spread","volume":"27","author":"Alabdulrazzaq","year":"2021","journal-title":"Results Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"106610","DOI":"10.1016\/j.asoc.2020.106610","article-title":"Forecasting of COVID19 per regions using ARIMA models and polynomial functions","volume":"96","author":"Fujita","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107161","DOI":"10.1016\/j.asoc.2021.107161","article-title":"Forecasting the dynamics of cumulative COVID-19 cases (confirmed, recovered and deaths) for top-16 countries using statistical machine learning models: Auto-Regressive Integrated Moving Average (ARIMA) and Seasonal Auto-Regressive Integrated Moving Average (SARIMA)","volume":"103","author":"ArunKumar","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"e262","DOI":"10.1016\/S1470-2045(19)30149-4","article-title":"Big data and machine learning algorithms for health-care delivery","volume":"20","author":"Ngiam","year":"2019","journal-title":"Lancet Oncol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1038\/s41591-018-0316-z","article-title":"A guide to deep learning in healthcare","volume":"25","author":"Esteva","year":"2019","journal-title":"Nat. Med."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1080\/17460441.2018.1547278","article-title":"An overview of neural networks for drug discovery and the inputs used","volume":"13","author":"Xu","year":"2018","journal-title":"Expert Opin. Drug Discov."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.neucom.2021.10.035","article-title":"Time series predicting of COVID-19 based on deep learning","volume":"468","author":"Alassafi","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1308\/147870804290","article-title":"Artificial intelligence in medicine","volume":"86","author":"Ramesh","year":"2004","journal-title":"Ann. R Coll Surg. Engl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"374","DOI":"10.2174\/138161282504190516080951","article-title":"Neural Networks in Neurological and Psychiatric Diseases","volume":"25","author":"Werner","year":"2019","journal-title":"Curr. Pharm. Des."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hessler, G., and Baringhaus, K.H. (2018). Artificial Intelligence in Drug Design. Molecules, 23.","DOI":"10.3390\/molecules23102520"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"100025","DOI":"10.1016\/j.cmpbup.2021.100025","article-title":"Role of deep learning in early detection of COVID-19: Scoping review","volume":"1","author":"Alzubaidi","year":"2021","journal-title":"Comput. Methods Programs Biomed. Update"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.conb.2019.01.007","article-title":"Analyzing biological and artificial neural networks: Challenges with opportunities for synergy?","volume":"55","author":"Barrett","year":"2019","journal-title":"Curr. Opin. Neurobiol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2451","DOI":"10.1162\/089976600300015015","article-title":"Learning to forget: Continual prediction with LSTM","volume":"12","author":"Gers","year":"2000","journal-title":"Neural Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"100566","DOI":"10.1016\/j.imu.2021.100566","article-title":"COVID-19 prediction using LSTM algorithm: GCC case study","volume":"23","author":"Ghany","year":"2021","journal-title":"Inf. Med. Unlocked"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"109864","DOI":"10.1016\/j.chaos.2020.109864","article-title":"Time series forecasting of COVID-19 transmission in Canada using LSTM networks","volume":"135","author":"Chimmula","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"104495","DOI":"10.1016\/j.rinp.2021.104495","article-title":"Time series forecasting of new cases and new deaths rate for COVID-19 using deep learning methods","volume":"27","author":"Ayoobi","year":"2021","journal-title":"Results Phys."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wilkosz, M., and Szczesna, A. (2021). Multi-Headed Conv-LSTM Network for Heart Rate Estimation during Daily Living Activities. Sensors, 21.","DOI":"10.3390\/s21155212"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4688","DOI":"10.1109\/TNNLS.2019.2957276","article-title":"Neural Machine Translation With GRU-Gated Attention Model","volume":"31","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zhao, C., You, J., Wen, X., and Li, X. (2020). Deep Bi-LSTM Networks for Sequential Recommendation. Entropy, 22.","DOI":"10.3390\/e22080870"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"110121","DOI":"10.1016\/j.chaos.2020.110121","article-title":"Deep learning methods for forecasting COVID-19 time-Series data: A Comparative study","volume":"140","author":"Zeroual","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"110227","DOI":"10.1016\/j.chaos.2020.110227","article-title":"Time series forecasting of Covid-19 using deep learning models: India-USA comparative case study","volume":"140","author":"Shastri","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"17421","DOI":"10.1038\/s41598-021-97037-5","article-title":"The prediction and analysis of COVID-19 epidemic trend by combining LSTM and Markov method","volume":"11","author":"Ma","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_41","first-page":"11881","article-title":"Deep learning via LSTM models for COVID-19 infection forecasting in India","volume":"2101","author":"Chandra","year":"2021","journal-title":"CoRR"},{"key":"ref_42","unstructured":"Ritchie, H., Mathieu, E., Rod\u00e9s-Guirao, L., Appel, C., Giattino, C., Ortiz-Ospina, E., Hasell, J., Macdonald, B., Beltekian, D., and Roser, M. (2022, May 18). Coronavirus Pandemic (COVID-19). Our World in Data. Available online: https:\/\/ourworldindata.org\/coronavirus."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.ijid.2021.10.007","article-title":"Predicting the effective reproduction number of COVID-19: Inference using human mobility, temperature, and risk awareness","volume":"113","author":"Jung","year":"2021","journal-title":"Int. J. Infect. Dis."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Huisman, J.S., Scire, J., Angst, D.C., Li, J., Neher, R.A., Maathuis, M.H., Bonhoeffer, S., and Stadler, T. (2021). Estimation and worldwide monitoring of the effective reproductive number of SARS-CoV-2. medRxiv.","DOI":"10.1101\/2020.11.26.20239368"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1093\/aje\/kwt133","article-title":"A New Framework and Software to Estimate Time-Varying Reproduction Numbers During Epidemics","volume":"178","author":"Cori","year":"2013","journal-title":"Am. J. Epidemiol."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"8495288","DOI":"10.1155\/2021\/8495288","article-title":"Prediction of Short-Term Stock Price Trend Based on Multiview RBF Neural Network","volume":"2021","author":"Lv","year":"2021","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Nabipour, M., Nayyeri, P., Jabani, H., Mosavi, A., Salwana, E., and S, S. (2020). Deep Learning for Stock Market Prediction. Entropy, 22.","DOI":"10.20944\/preprints202003.0256.v1"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Chandra, R., and He, Y. (2021). Bayesian neural networks for stock price forecasting before and during COVID-19 pandemic. PLoS ONE, 16.","DOI":"10.1371\/journal.pone.0253217"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Reid, D., Hussain, A.J., and Tawfik, H. (2014). Financial time series prediction using spiking neural networks. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0103656"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"R231","DOI":"10.1016\/j.cub.2019.02.034","article-title":"Neural network models and deep learning","volume":"29","author":"Kriegeskorte","year":"2019","journal-title":"Curr. Biol."},{"key":"ref_51","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A Method for Stochastic Optimization. arXiv."},{"key":"ref_52","unstructured":"Van Rossum, G., and Drake, F.L. (2009). Python 3 Reference Manual, CreateSpace."},{"key":"ref_53","unstructured":"McKinney, W. (July, January 28). Data Structures for Statistical Computing in Python. Proceedings of the 9th Python in Science Conference, Austin, TX, USA."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1038\/s41586-020-2649-2","article-title":"Array programming with NumPy","volume":"585","author":"Harris","year":"2020","journal-title":"Nature"},{"key":"ref_55","unstructured":"Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., and Devin, M. (2016). TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems. arXiv."},{"key":"ref_56","first-page":"2825","article-title":"Scikit-learn: Machine Learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Bisong, E. (2019). Google Colaboratory. Building Machine Learning and Deep Learning Models on Google Cloud Platform: A Comprehensive Guide for Beginners, Apress.","DOI":"10.1007\/978-1-4842-4470-8"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"103791","DOI":"10.1016\/j.jbi.2021.103791","article-title":"Comparative study of machine learning methods for COVID-19 transmission forecasting","volume":"118","author":"Dairi","year":"2021","journal-title":"J. Biomed. Inf."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"e201664","DOI":"10.1001\/jamanetworkopen.2020.1664","article-title":"Evaluation of Deep Learning Models for Identifying Surgical Actions and Measuring Performance","volume":"3","author":"Khalid","year":"2020","journal-title":"JAMA Netw. Open"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"e623","DOI":"10.7717\/peerj-cs.623","article-title":"The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation","volume":"7","author":"Chicco","year":"2021","journal-title":"PeerJ Comput. Sci."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.neucom.2015.12.114","article-title":"Mean Absolute Percentage Error for regression models","volume":"192","author":"Golden","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1080\/00220970009600095","article-title":"Improving the Root Mean Square Error of Approximation for Nonnormal Conditions in Structural Equation Modeling","volume":"68","author":"Nevitt","year":"2000","journal-title":"J. Exp. Educ."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1097\/00006324-200302000-00005","article-title":"Visual acuity as a function of Zernike mode and level of root mean square error","volume":"80","author":"Applegate","year":"2003","journal-title":"Optom. Vis. Sci."},{"key":"ref_64","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_65","doi-asserted-by":"crossref","first-page":"407","DOI":"10.4103\/aca.ACA_94_19","article-title":"-test, analysis of variance, and covariance","volume":"22","author":"Mishra","year":"2019","journal-title":"Ann. Card Anaesth"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/7\/929\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:42:34Z","timestamp":1760139754000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/7\/929"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,4]]},"references-count":65,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["e24070929"],"URL":"https:\/\/doi.org\/10.3390\/e24070929","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,4]]}}}