{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T15:38:01Z","timestamp":1777217881906,"version":"3.51.4"},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2024,8,17]],"date-time":"2024-08-17T00:00:00Z","timestamp":1723852800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,8,17]],"date-time":"2024-08-17T00:00:00Z","timestamp":1723852800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"J.Alzabut, Prince Sultan University, Saudi Arabia and OSTIM University"},{"name":"G.Rajchakit","award":["National Research Council of Thailand (Talented Mid-Career Researchers) Grant Number 652505010733"],"award-info":[{"award-number":["National Research Council of Thailand (Talented Mid-Career Researchers) Grant Number 652505010733"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. &amp; Cyber."],"published-print":{"date-parts":[[2025,10]]},"DOI":"10.1007\/s13042-024-02301-5","type":"journal-article","created":{"date-parts":[[2024,8,17]],"date-time":"2024-08-17T00:02:00Z","timestamp":1723852920000},"page":"7045-7058","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Modeling the dynamics of Covid-19 in Japan: employing data-driven deep learning approach"],"prefix":"10.1007","volume":"16","author":[{"given":"S. Patrick","family":"Nelson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"Raja","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Eswaran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Alzabut","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Rajchakit","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,8,17]]},"reference":[{"key":"2301_CR1","unstructured":"https:\/\/www.worldometers.info\/coronavirus\/"},{"key":"2301_CR2","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2020.110256","volume":"139","author":"S Ahmad","year":"2020","unstructured":"Ahmad S, Ullah A, Al-Mdallal QM, Khan H, Shah K, Khan A (2020) Fractional order mathematical modeling of COVID-19 transmission. Chaos Solitons Fractals 139:110256","journal-title":"Chaos Solitons Fractals"},{"issue":"4\u20135","key":"2301_CR3","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/0925-2312(93)90006-O","volume":"5","author":"SI Amari","year":"1993","unstructured":"Amari SI (1993) Backpropagation and stochastic gradient descent method. Neurocomputing 5(4\u20135):185\u2013196","journal-title":"Neurocomputing"},{"key":"2301_CR4","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1109\/OJEMB.2020.3019758","volume":"1","author":"MA Bahloul","year":"2020","unstructured":"Bahloul MA, Chahid A, Laleg-Kirati TM (2020) Fractional-order seiqrdp model for simulating the dynamics of COVID-19 epidemic. IEEE Open J Eng Med Biol 1:249\u2013256","journal-title":"IEEE Open J Eng Med Biol"},{"issue":"1","key":"2301_CR5","first-page":"5595","volume":"18","author":"AG Baydin","year":"2017","unstructured":"Baydin AG, Pearlmutter BA, Radul AA, Siskind JM (2017) Automatic differentiation in machine learning: a survey. J Mach Learn Res 18(1):5595\u20135637","journal-title":"J Mach Learn Res"},{"key":"2301_CR6","doi-asserted-by":"crossref","unstructured":"Berkhahn S, Ehrhardt M (2022) A physics-informed neural network to model COVID-19 infection and hospitalization scenarios. In: Advances in continuous and discrete models, vol 61","DOI":"10.1186\/s13662-022-03733-5"},{"key":"2301_CR7","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/978-3-642-93454-4","volume-title":"Mathematical and statistical approaches to AIDS epidemiology","author":"CC Chavez","year":"1989","unstructured":"Chavez CC (1989) Mathematical and statistical approaches to AIDS epidemiology, vol 83. Springer, Berlin, pp 2\u201335"},{"key":"2301_CR8","volume":"135","author":"VKR Chimmula","year":"2020","unstructured":"Chimmula VKR, Zhang L (2020) Time series forecasting of Covid-19 transmission in Canada using LSTM networks. Chaos Solitons Fractals 135:109864","journal-title":"Chaos Solitons Fractals"},{"issue":"5","key":"2301_CR9","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1007\/s11538-008-9299-0","volume":"70","author":"N Chitnis","year":"2008","unstructured":"Chitnis N, Hyman JM, Cushing JM (2008) Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull Math Biol 70(5):1272\u20131296","journal-title":"Bull Math Biol"},{"issue":"2","key":"2301_CR10","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/j.mbs.2006.11.011","volume":"208","author":"G Chowell","year":"2007","unstructured":"Chowell G, Duenas PD, Miller JC, Velazco AA, Hyman JM, Fenimore PW, Chavez CC (2007) Estimation of the reproduction number of dengue fever from spatial epidemic data. Math Biosci 208(2):571\u2013589","journal-title":"Math Biosci"},{"key":"2301_CR11","doi-asserted-by":"crossref","DOI":"10.1016\/j.rinp.2020.103642","volume":"19","author":"CT Deressa","year":"2020","unstructured":"Deressa CT, Mussa YO, Duressa GF (2020) Optimal control and sensitivity analysis for transmission dynamics of Coronavirus. Results Phys 19:103642","journal-title":"Results Phys"},{"issue":"4","key":"2301_CR12","doi-asserted-by":"crossref","first-page":"845","DOI":"10.3390\/sym15040845","volume":"15","author":"J Dianavinnarasi","year":"2023","unstructured":"Dianavinnarasi J, Raja R, Alzabut J, Jose SA, Khan H (2023) Fractional order-density dependent mathematical model to find the better strain of Wolbachia. Symmetry 15(4):845","journal-title":"Symmetry"},{"key":"2301_CR13","doi-asserted-by":"crossref","DOI":"10.1002\/9781118625590","volume-title":"Applied regression analysis","author":"NR Draper","year":"1998","unstructured":"Draper NR, Smith H (1998) Applied regression analysis. Wiley, Hoboken"},{"key":"2301_CR14","volume-title":"Primer of applied regression and analysis of variance","author":"SA Glantz","year":"2001","unstructured":"Glantz SA, Slinker BK, Neilands TB (2001) Primer of applied regression and analysis of variance. McGraw-Hill, Medical Pub. Division, New York"},{"key":"2301_CR15","unstructured":"Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press. http:\/\/www.deeplearningbook.org"},{"issue":"2","key":"2301_CR16","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0893-6080(91)90009-T","volume":"4","author":"K Hornik","year":"1991","unstructured":"Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4(2):251\u2013257","journal-title":"Neural Netw"},{"key":"2301_CR17","volume":"84","author":"SA Jose","year":"2023","unstructured":"Jose SA, Raja R, Dianavinnarasi J, Baleanu D, Jirawattanapanit A (2023) Mathematical modeling of chickenpox in Phuket: efficacy of precautionary measures and bifurcation analysis. Biomed Signal Process Control 84:104714","journal-title":"Biomed Signal Process Control"},{"key":"2301_CR18","doi-asserted-by":"crossref","first-page":"4879","DOI":"10.1007\/s11071-022-08063-5","volume":"111","author":"SA Jose","year":"2023","unstructured":"Jose SA, Raja R, Omede BI, Agarwal RP, Alzabut J, Cao J, Balas VE (2023) Mathematical modeling on co-infection: transmission dynamics of Zika virus and Dengue fever. Nonlinear Dyn 111:4879\u20134914","journal-title":"Nonlinear Dyn"},{"key":"2301_CR19","unstructured":"Ke J, Ma J, Yin X, Singh R (2022) Simulation and application of COVID-19 compartmental model using Physics-informed Neural Network. ArXiv arXiv:2208.02433"},{"issue":"772","key":"2301_CR20","first-page":"700","volume":"115","author":"WO Kermack","year":"1927","unstructured":"Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc R Soc Lond Ser A Contain Pap Math Phys Charact 115(772):700\u2013721","journal-title":"Proc R Soc Lond Ser A Contain Pap Math Phys Charact"},{"key":"2301_CR21","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1038\/s43588-021-00158-0","volume":"1","author":"E Kharazmi","year":"2021","unstructured":"Kharazmi E, Cai M, Zheng X, Lin G, Karniadakis GE (2021) Identifiability and predictability of integer-and fractional-order epidemiological models using physics-informed neural networks. Nat Comput Sci 1:744\u2013753","journal-title":"Nat Comput Sci"},{"key":"2301_CR22","unstructured":"Kingma DP, Ba J (2014) Adam: a method for stochastic optimization. Computing Research Repository 1412"},{"issue":"23","key":"2301_CR23","doi-asserted-by":"crossref","first-page":"8316","DOI":"10.3390\/app10238316","volume":"10","author":"K Kozio\u0142","year":"2020","unstructured":"Kozio\u0142 K, Stanis\u0142awski R, Bialic G (2020) Fractional-order sir epidemic model for transmission prediction of COVID-19 disease. Appl Sci 10(23):8316","journal-title":"Appl Sci"},{"issue":"1","key":"2301_CR24","first-page":"249","volume":"316","author":"V Lakshmikantham","year":"1995","unstructured":"Lakshmikantham V, Leela S, Martynyuk AA (1995) Stability analysis of nonlinear systems. Springer Link 316(1):249\u2013275","journal-title":"Springer Link"},{"issue":"3","key":"2301_CR25","doi-asserted-by":"crossref","first-page":"753","DOI":"10.3934\/mbe.2011.8.753","volume":"8","author":"J Li","year":"2011","unstructured":"Li J (2011) Malaria model with stage-structured mosquitoes. Math Bioscie Eng 8(3):753","journal-title":"Math Bioscie Eng"},{"issue":"1","key":"2301_CR26","first-page":"1","volume":"3","author":"CY Lin","year":"2020","unstructured":"Lin CY (2020) Social reaction toward the 2019 novel coronavirus (COVID-19). Soc Health Behav 3(1):1\u20132","journal-title":"Soc Health Behav"},{"issue":"8","key":"2301_CR27","doi-asserted-by":"crossref","first-page":"1617","DOI":"10.1080\/00207160.2021.1929942","volume":"98","author":"J Long","year":"2021","unstructured":"Long J, Khaliq AQM, Furati KM (2021) Identification and prediction of time-varying parameters of COVID-19 model: a data-driven deep learning approach. Int J Comput Math 98(8):1617\u20131632","journal-title":"Int J Comput Math"},{"key":"2301_CR28","doi-asserted-by":"crossref","first-page":"103746","DOI":"10.1016\/j.rinp.2020.103746","volume":"21","author":"L Lopez","year":"2021","unstructured":"Lopez L, Rodo X (2021) A modified SEIR model to predict the COVID-19 outbreak in Spain and Italy: simulating control scenarios and multi-scale epidemics. Results Phys 21:103746","journal-title":"Results Phys"},{"issue":"1","key":"2301_CR29","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1137\/19M1274067","volume":"63","author":"L Lu","year":"2021","unstructured":"Lu L, Meng X, Mao Z, Karniadakis GE (2021) DeepXDE: a deep learning library for solving differential equations. SIAM Rev 63(1):208\u2013228","journal-title":"SIAM Rev"},{"key":"2301_CR30","doi-asserted-by":"crossref","first-page":"1572","DOI":"10.1002\/int.22686","volume":"37","author":"S Lu","year":"2022","unstructured":"Lu S, Zhu Z, Gorriz JM, Wang SH, Zhang YD (2022) NAGNN: classification of COVID-19 based on neighboring aware representation from deep graph neural network. Int J Intell Syst 37:1572\u20131598","journal-title":"Int J Intell Syst"},{"key":"2301_CR31","volume":"109","author":"SY Lu","year":"2021","unstructured":"Lu SY, Nayak DR, Wang SH, Zhang YD (2021) A cerebral microbleed diagnosis method via FeatureNet and ensembled randomized neural networks. Appl Soft Comput 109:107567","journal-title":"Appl Soft Comput"},{"issue":"1","key":"2301_CR32","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1016\/j.jmaa.2015.09.048","volume":"434","author":"J Luo","year":"2016","unstructured":"Luo J, Wang W, Chen H, Fu R (2016) Bifurcations of a mathematical model for HIV dynamics. J Math Anal Appl 434(1):837\u2013857","journal-title":"J Math Anal Appl"},{"key":"2301_CR33","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/978-1-4899-7612-3","volume-title":"An introduction to mathematical epidemiology","author":"M Martcheva","year":"2015","unstructured":"Martcheva M (2015) An introduction to mathematical epidemiology. Springer, Berlin, p 61"},{"key":"2301_CR34","doi-asserted-by":"crossref","unstructured":"Molina E, Viale L, Vazquez P (2022) How should we design violin plots? In: 2022 IEEE 4th workshop on visualization guidelines in research, design, and education (VisGuides)","DOI":"10.1109\/VisGuides57787.2022.00006"},{"issue":"1","key":"2301_CR35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1515\/cmb-2022-0001","volume":"10","author":"L Nguyen","year":"2022","unstructured":"Nguyen L, Raissi M, Seshaiyer P (2022) Modeling, analysis and physics informed neural network approaches for studying the dynamics of COVID-19 involving human\u2013human and human\u2013pathogen interaction. Comput Math Biophys 10(1):1\u201317","journal-title":"Comput Math Biophys"},{"key":"2301_CR36","volume":"2014","author":"SCO Noutchie","year":"2014","unstructured":"Noutchie SCO, Mugisha S (2014) A fractional SEIR epidemic model for spatial and temporal spread of measles in metapopulations. Abstr Appl Anal 2014:781028","journal-title":"Abstr Appl Anal"},{"issue":"4","key":"2301_CR37","doi-asserted-by":"crossref","first-page":"471","DOI":"10.3390\/epidemiologia2040033","volume":"2","author":"KD Olumoyin","year":"2021","unstructured":"Olumoyin KD, Khaliq AQM, Furati KM (2021) Data-driven deep-learning algorithm for asymptomatic COVID-19 model with varying mitigation measures and transmission rate. Epidemiologia 2(4):471\u2013489","journal-title":"Epidemiologia"},{"issue":"1","key":"2301_CR38","doi-asserted-by":"crossref","first-page":"148","DOI":"10.30707\/LiB4.1Padmanabhan","volume":"4","author":"P Padmanabhan","year":"2017","unstructured":"Padmanabhan P, Seshaiyer P, Chavez CC (2017) Mathematical modeling, analysis and simulation of the spread of Zika with influence of sexual transmission and preventive measures. Lett Biomath 4(1):148\u2013166","journal-title":"Lett Biomath"},{"issue":"6481","key":"2301_CR39","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1126\/science.aaw4741","volume":"367","author":"M Raissi","year":"2020","unstructured":"Raissi M, Yazdani A, Karniadakis GE (2020) Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations. Science 367(6481):1026\u20131030","journal-title":"Science"},{"key":"2301_CR40","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","volume":"378","author":"M Raissi","year":"2019","unstructured":"Raissi M, Perdikaris P, Karniadakis GE (2019) Physics informed deep learning: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378:686\u2013707","journal-title":"J Comput Phys"},{"issue":"2","key":"2301_CR41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.30707\/LiB6.2Raissi","volume":"6","author":"M Raissi","year":"2019","unstructured":"Raissi M, Ramezani N, Seshaiyer P (2019) On parameter estimation approaches for predicting disease transmission through optimization, deep learning and statistical inference methods. Lett Biomath 6(2):1\u201326","journal-title":"Lett Biomath"},{"key":"2301_CR42","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1007\/s11071-020-05757-6","volume":"101","author":"K Rajagopal","year":"2020","unstructured":"Rajagopal K, Hasanzadeh N, Parastesh F, Hamarash II, Jafari S, Hussain I (2020) A fractional-order model for the novel coronavirus (COVID-19) outbreak. Nonlinear Dyn 101:711\u2013718","journal-title":"Nonlinear Dyn"},{"key":"2301_CR43","doi-asserted-by":"crossref","first-page":"6664483","DOI":"10.1155\/2021\/6664483","volume":"2021","author":"P Riyapan","year":"2021","unstructured":"Riyapan P, Shuaib SE, Intarasit A (2021) A mathematical model of COVID-19 pandemic: a case study of Bangkok, Thailand. Comput Math Methods Med 2021:6664483","journal-title":"Comput Math Methods Med"},{"key":"2301_CR44","volume":"537","author":"CY Sang","year":"2020","unstructured":"Sang CY, Liao SG (2020) Modeling and simulation of information dissemination model considering user\u2019s awareness behavior in mobile social networks. Physica A 537:122639","journal-title":"Physica A"},{"key":"2301_CR45","first-page":"71","volume":"9","author":"S Shaier","year":"2021","unstructured":"Shaier S, Raissi M, Seshaiyer P (2021) Data-driven approaches for predicting spread of infectious diseases through DINNs: disease informed neural networks. Lett Biomath 9:71\u2013105","journal-title":"Lett Biomath"},{"key":"2301_CR46","unstructured":"Shin Y, Darbon J, Karniadakis GE (2020) On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs. arXiv:2004.01806"},{"issue":"40","key":"2301_CR47","first-page":"84","volume":"2019","author":"SO Sowole","year":"2019","unstructured":"Sowole SO, Sangare D, Ibrahim AA, Paul IA (2019) On the existence, uniqueness, stability of solution and numerical simulations of a mathematical model for measles disease. Int J Adv Math 2019(40):84\u2013111","journal-title":"Int J Adv Math"},{"key":"2301_CR48","unstructured":"Steel RGD, Torrie JH (1962) Principles and procedures of statistics. Biometrische Zeitschrift 4"},{"key":"2301_CR49","doi-asserted-by":"crossref","first-page":"100139","DOI":"10.1016\/j.prdoa.2022.100139","volume":"6","author":"A Sandri","year":"2022","unstructured":"Sandri A, Di Vico IA, Riello M, Marotta A, Tinazzi M (2022) The impact of recurrent Covid-19 waves on patients with functional movement disorders: a follow-up study. Clin Parkinsonism Relat Disord 6:100139","journal-title":"Clin Parkinsonism Relat Disord"},{"issue":"8","key":"2301_CR50","doi-asserted-by":"crossref","first-page":"2250059","DOI":"10.1142\/S1793524522500590","volume":"15","author":"R Thomas","year":"2022","unstructured":"Thomas R, Jose SA, Raja R, Alzabut J, Cao J, Balas VE (2022) Modeling and analysis of SEIRS epidemic models using homotopy perturbation method: a special outlook to 2019-nCoV in India. Int J Biomath 15(8):2250059","journal-title":"Int J Biomath"},{"issue":"11","key":"2301_CR51","doi-asserted-by":"crossref","first-page":"e1007575","DOI":"10.1371\/journal.pcbi.1007575","volume":"16","author":"A Yazdani","year":"2020","unstructured":"Yazdani A, Lu L, Raissi M, Karniadakis GE (2020) Systems biology informed deep learning for inferring parameters and hidden dynamics. PLoS Comput Biol 16(11):e1007575","journal-title":"PLoS Comput Biol"},{"key":"2301_CR52","doi-asserted-by":"crossref","DOI":"10.1016\/j.inffus.2023.101859","volume":"98","author":"Y Zhang","year":"2023","unstructured":"Zhang Y, Deng L, Zhu H, Wang W, Ren Z, Zhou Q, Lu S, Sun S, Zhu Z, Gorriz JM, Wang S (2023) Deep learning in food category recognition. Inf Fusion 98:101859","journal-title":"Inf Fusion"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-024-02301-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13042-024-02301-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-024-02301-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T16:57:25Z","timestamp":1760547445000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13042-024-02301-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,17]]},"references-count":52,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2025,10]]}},"alternative-id":["2301"],"URL":"https:\/\/doi.org\/10.1007\/s13042-024-02301-5","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"value":"1868-8071","type":"print"},{"value":"1868-808X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,17]]},"assertion":[{"value":"21 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 August 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}