{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T03:01:18Z","timestamp":1785466878967,"version":"3.56.0"},"reference-count":43,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/100012908","name":"Indian Institute of Engineering Science and Technology, Shibpur","doi-asserted-by":"publisher","award":["107\/ACAD\/2022"],"award-info":[{"award-number":["107\/ACAD\/2022"]}],"id":[{"id":"10.13039\/100012908","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.matcom.2026.04.026","type":"journal-article","created":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T23:35:01Z","timestamp":1776814501000},"page":"337-361","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["Theoretical investigation of tuberculosis transmission dynamics: A soft computing\u2013integrated mathematical approach"],"prefix":"10.1016","volume":"248","author":[{"given":"Sathi","family":"Patra","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0123-9940","authenticated-orcid":false,"given":"Soovoojeet","family":"Jana","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tapan Kumar","family":"Kar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.matcom.2026.04.026_b1","series-title":"Tuberculosis","author":"World Health Organization","year":"2024"},{"key":"10.1016\/j.matcom.2026.04.026_b2","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.physa.2018.01.014","article-title":"Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation","volume":"497","author":"Khajanchi","year":"2018","journal-title":"Phys. A"},{"issue":"3","key":"10.1016\/j.matcom.2026.04.026_b3","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1006\/tpbi.2000.1451","article-title":"A model for tuberculosis with exogenous reinfection","volume":"57","author":"Feng","year":"2000","journal-title":"Theor. Popul. Biology"},{"issue":"10","key":"10.1016\/j.matcom.2026.04.026_b4","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1016\/S1473-3099(05)70240-1","article-title":"Exogenous reinfection in tuberculosis","volume":"5","author":"Chiang","year":"2005","journal-title":"Lancet Infect. Dis."},{"key":"10.1016\/j.matcom.2026.04.026_b5","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.chaos.2019.01.025","article-title":"Stability and bifurcation analysis of an epidemic model with the effect of media","volume":"120","author":"Kar","year":"2019","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.04.026_b6","series-title":"An Introduction to Mathematical Epidemiology","author":"Martcheva","year":"2015"},{"key":"10.1016\/j.matcom.2026.04.026_b7","article-title":"A fractional-order mathematical approach to dengue transmission: Encompassing genetic algorithm-based optimization","volume":"14","author":"Patra","year":"2025","journal-title":"J. Comput. Appl. Math."},{"issue":"9","key":"10.1016\/j.matcom.2026.04.026_b8","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s40435-025-01800-9","article-title":"Impact of vaccination and media on a Caputo derivative-based fractional-order epidemic model with PRCC analysis: S. Barman et al.","volume":"13","author":"Barman","year":"2025","journal-title":"Int. J. Dyn. Control."},{"issue":"2","key":"10.1016\/j.matcom.2026.04.026_b9","doi-asserted-by":"crossref","first-page":"361","DOI":"10.3934\/mbe.2004.1.361","article-title":"Dynamical models of tuberculosis and their applications","volume":"1","author":"Castillo-Chavez","year":"2004","journal-title":"Math. Biosci. Eng."},{"issue":"3","key":"10.1016\/j.matcom.2026.04.026_b10","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1006\/tpbi.2000.1451","article-title":"A model for tuberculosis with exogenous reinfection","volume":"57","author":"Feng","year":"2000","journal-title":"Theor. Popul. Biology"},{"issue":"3","key":"10.1016\/j.matcom.2026.04.026_b11","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s40435-013-0020-2","article-title":"Mathematical modelling of TB with the effects of case detection and treatment","volume":"1","author":"Athithan","year":"2013","journal-title":"Int. J. Dyn. Control."},{"key":"10.1016\/j.matcom.2026.04.026_b12","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1016\/j.matcom.2023.09.021","article-title":"Qualitative analysis of TB transmission dynamics considering both the age since latency and relapse","volume":"225","author":"Das","year":"2024","journal-title":"Math. Comput. Simulation"},{"key":"10.1016\/j.matcom.2026.04.026_b13","doi-asserted-by":"crossref","DOI":"10.1016\/j.amc.2019.124732","article-title":"The impact of the media awareness and optimal strategy on the prevalence of tuberculosis","volume":"366","author":"Das","year":"2020","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.matcom.2026.04.026_b14","series-title":"Neurocomputing: Foundations of Research","first-page":"123","article-title":"Adaptive switching circuits","author":"Widrow","year":"1988"},{"key":"10.1016\/j.matcom.2026.04.026_b15","series-title":"Perceptrons, Reissue of the 1988 Expanded Edition with a New Foreword By L\u00c9on Bottou: An Introduction to Computational Geometry","author":"Minsky","year":"2017"},{"key":"10.1016\/j.matcom.2026.04.026_b16","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"Raissi","year":"2019","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.matcom.2026.04.026_b17","first-page":"14453","article-title":"Einns: epidemiologically-informed neural networks","volume":"vol. 37","author":"Rodr\u00edguez","year":"2023"},{"key":"10.1016\/j.matcom.2026.04.026_b18","doi-asserted-by":"crossref","DOI":"10.1016\/j.jocs.2024.102470","article-title":"Deep learning aided surrogate modeling of the epidemiological models","volume":"84","author":"Kurul","year":"2025","journal-title":"J. Comput. Sci."},{"key":"10.1016\/j.matcom.2026.04.026_b19","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2024.111957","article-title":"Neural network approach for cholera dynamics: Integrating deterministic and stochastic insights","volume":"296","author":"Shah","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"10.1016\/j.matcom.2026.04.026_b20","first-page":"1","article-title":"A novel numerical framework for stochastic tuberculosis modeling with treatment via neural network and spectral method","volume":"20","author":"Iqbal","year":"2025","journal-title":"J. Appl. Math. Comput."},{"key":"10.1016\/j.matcom.2026.04.026_b21","doi-asserted-by":"crossref","first-page":"395","DOI":"10.3389\/fmicb.2019.00395","article-title":"Artificial neural networks for prediction of tuberculosis disease","volume":"10","author":"Khan","year":"2019","journal-title":"Front. Microbiol."},{"key":"10.1016\/j.matcom.2026.04.026_b22","series-title":"TimeNet: Pre-trained deep recurrent neural network for time series classification","author":"Malhotra","year":"2017"},{"key":"10.1016\/j.matcom.2026.04.026_b23","article-title":"Neural ordinary differential equations","volume":"31","author":"Chen","year":"2018","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.matcom.2026.04.026_b24","doi-asserted-by":"crossref","DOI":"10.1016\/j.compchemeng.2021.107403","article-title":"Comparison of the performance of different metaheuristic methods for the optimization of shell-and-tube heat exchangers","volume":"152","author":"Lara-Monta\u00f1o","year":"2021","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.matcom.2026.04.026_b25","doi-asserted-by":"crossref","unstructured":"J.J. Grefenstette, Genetic algorithms and machine learning, in: Proceedings of the Sixth Annual Conference on Computational Learning Theory, 1993, pp. 3\u20134.","DOI":"10.1145\/168304.168305"},{"key":"10.1016\/j.matcom.2026.04.026_b26","doi-asserted-by":"crossref","first-page":"17153","DOI":"10.1007\/s00500-020-05009-0","article-title":"Water management using genetic algorithm-based machine learning","volume":"24","author":"Gino Sophia","year":"2020","journal-title":"Soft Comput."},{"key":"10.1016\/j.matcom.2026.04.026_b27","first-page":"2412","article-title":"Application of genetic algorithms in machine learning","volume":"2","author":"Bhasin","year":"2011","journal-title":"IJCSIT"},{"key":"10.1016\/j.matcom.2026.04.026_b28","doi-asserted-by":"crossref","first-page":"2279","DOI":"10.1016\/j.istruc.2021.04.018","article-title":"Bond strength prediction of concrete-encased steel structures using hybrid machine learning method","volume":"32","author":"Wang","year":"2021","journal-title":"Structures"},{"key":"10.1016\/j.matcom.2026.04.026_b29","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2020.109883","article-title":"Optimal policies for control of the novel coronavirus disease (COVID-19) outbreak","volume":"136","author":"Yousefpour","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.04.026_b30","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1023\/A:1022627411411","article-title":"Support-vector networks","volume":"20","author":"Vapnik","year":"1995","journal-title":"Mach. Learn."},{"key":"10.1016\/j.matcom.2026.04.026_b31","doi-asserted-by":"crossref","DOI":"10.1016\/j.rinp.2021.104991","article-title":"Mathematical analysis of a social hierarchy-structured model for malaria transmission dynamics","volume":"34","author":"Olaniyi","year":"2022","journal-title":"Results Phys."},{"key":"10.1016\/j.matcom.2026.04.026_b32","doi-asserted-by":"crossref","DOI":"10.1088\/1402-4896\/acae64","article-title":"Transmission dynamics of monkeypox virus with treatment and vaccination controls: a fractional order mathematical approach","volume":"98","author":"Majee","year":"2023","journal-title":"Phys. Scr."},{"key":"10.1016\/j.matcom.2026.04.026_b33","first-page":"1","article-title":"Complex dynamics of a host-vector dynamics of dengue infection incorporating optimal control strategy with cost-effectiveness: a fractional-order derivative method","author":"Patra","year":"2025","journal-title":"J. Math. Sci."},{"key":"10.1016\/j.matcom.2026.04.026_b34","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2019.109450","article-title":"Transmission dynamics of tuberculosis with multiple re-infections","volume":"130","author":"Das","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.04.026_b35","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2021.110879","article-title":"Global dynamics of a tuberculosis model with sensitivity of the smear microscopy","volume":"146","author":"Das","year":"2021","journal-title":"Chaos Solitons Fractals"},{"issue":"86","key":"10.1016\/j.matcom.2026.04.026_b36","doi-asserted-by":"crossref","DOI":"10.1098\/rsif.2012.1018","article-title":"Sensitivity analysis of infectious disease models: methods, advances and their application","volume":"10","author":"Wu","year":"2013","journal-title":"J. R. Soc. Interface"},{"issue":"16","key":"10.1016\/j.matcom.2026.04.026_b37","doi-asserted-by":"crossref","DOI":"10.1142\/S0218127423501924","article-title":"Complex dynamics and fractional-order optimal control of an epidemic model with saturated treatment and incidence","volume":"33","author":"Majee","year":"2023","journal-title":"Int. J. Bifurc. Chaos"},{"issue":"1","key":"10.1016\/j.matcom.2026.04.026_b38","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1007\/s40435-023-01348-6","article-title":"Modeling and analysis of Caputo-type fractional-order SEIQR epidemic model","volume":"12","author":"Majee","year":"2024","journal-title":"Int. J. Dyn. Control."},{"issue":"1","key":"10.1016\/j.matcom.2026.04.026_b39","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.jtbi.2008.04.011","article-title":"A methodology for performing global uncertainty and sensitivity analysis in systems biology","volume":"254","author":"Marino","year":"2008","journal-title":"J. Theor. Biology"},{"key":"10.1016\/j.matcom.2026.04.026_b40","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.envsoft.2017.02.001","article-title":"Comparison of variance-based and moment-independent global sensitivity analysis approaches by application to the SWAT model","volume":"91","author":"Zadeh","year":"2017","journal-title":"Environ. Model. Softw."},{"issue":"253","key":"10.1016\/j.matcom.2026.04.026_b41","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1080\/01621459.1951.10500769","article-title":"The Kolmogorov\u2013Smirnov test for goodness of fit","volume":"46","author":"Massey, Jr.","year":"1951","journal-title":"J. Am. Stat. Assoc."},{"issue":"8","key":"10.1016\/j.matcom.2026.04.026_b42","doi-asserted-by":"crossref","first-page":"363","DOI":"10.3390\/axioms11080363","article-title":"Fractional dynamics of a measles epidemic model","volume":"11","author":"Abboubakar","year":"2022","journal-title":"Axioms"},{"issue":"2","key":"10.1016\/j.matcom.2026.04.026_b43","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1080\/21645515.2017.1264774","article-title":"Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology","volume":"13","author":"Bonin","year":"2017","journal-title":"Hum. Vaccines Immunother."}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426001680?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426001680?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T02:32:25Z","timestamp":1783045945000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475426001680"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":43,"alternative-id":["S0378475426001680"],"URL":"https:\/\/doi.org\/10.1016\/j.matcom.2026.04.026","relation":{},"ISSN":["0378-4754"],"issn-type":[{"value":"0378-4754","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Theoretical investigation of tuberculosis transmission dynamics: A soft computing\u2013integrated mathematical approach","name":"articletitle","label":"Article Title"},{"value":"Mathematics and Computers in Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.matcom.2026.04.026","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}]}}