{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T11:51:17Z","timestamp":1782388277414,"version":"3.54.5"},"reference-count":72,"publisher":"AIP Publishing","issue":"6","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,6,1]]},"abstract":"<jats:p>In this study, we develop a data-driven susceptible\u2013exposed\u2013infectious\u2013treatment tuberculosis transmission model. The model incorporates a Holling type-II saturated incidence rate to capture behavioral and contact saturation effects, along with a Verhulst-type treatment function to reflect constraints in treatment capacity. Model parameters are estimated using India\u2019s tuberculosis (TB) incidence data from 2000 to 2020, yielding R0\u2009=\u20091.4507, which indicates persistent disease transmission in the absence of effective interventions. To identify efficient control strategies, an optimal control problem is formulated by introducing three time-dependent interventions: preventive measures (u1), tuberculosis preventive treatment (u2), and active case finding (u3). The necessary optimality conditions are obtained using Pontryagin\u2019s maximum principle, and the resulting system is solved numerically. Two intervention scenarios are examined: a baseline scenario with limited intervention efficacy (\u03c4\u2009=\u20090.15, \u03b8\u2009=\u20090.05) and an enhanced scenario with improved efficacy parameters (\u03c4\u2009=\u20090.60, \u03b8\u2009=\u20090.67). A comprehensive cost-effectiveness analysis is conducted using incremental averted ratio, Average Cost-Effectiveness Ratio (ACER), and Incremental Cost-Effectiveness Ratio (ICER) to compare competing intervention strategies. The analysis shows that, under the baseline efficacy, strategy E (u1 only) emerges as the most impactful intervention for reducing transmission. Under the with-improvement scenario, strategy C (u1\u2009+\u2009u3) demonstrates the most economically efficient, achieving the lowest ACER and most favorable ICER among all strategies considered. These findings provide evidence-based, cost-effective intervention strategies to guide policy formulation and accelerate India\u2019s progress toward the WHO End TB strategy milestones, including a 95% reduction in TB deaths and 90% reduction in incidence by 2035 relative to 2015 levels.<\/jats:p>","DOI":"10.1063\/5.0332974","type":"journal-article","created":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T11:37:55Z","timestamp":1782387475000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["A data-driven tuberculosis model with behavioral changes and saturated treatment: Optimal control and cost-effectiveness study"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-0513-7899","authenticated-orcid":false,"given":"Pooja","family":"Khoda","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shaheed Bhagat Singh College, University of Delhi 1 , New Delhi 110017,","place":["India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tapan","family":"Sarkar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Presidency University, Itgalpura 2 , Bangalore, Karnataka 560064,","place":["India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4138-3621","authenticated-orcid":false,"given":"Om Prakash","family":"Meena","sequence":"additional","affiliation":[{"name":"School of Physical Sciences, Jawaharlal Nehru University (JNU) 3 , New Delhi 110067,","place":["India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9554-235X","authenticated-orcid":false,"given":"Sada Nand","family":"Prasad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dr. Bhim Rao Ambedkar College, University of Delhi 4 , New Delhi 110094,","place":["India"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,6,25]]},"reference":[{"issue":"1","key":"2026062507374694500_c1","doi-asserted-by":"publisher","first-page":"2323724","DOI":"10.1080\/17513758.2024.2323724","article-title":"Global dynamics of discrete mathematical models of tuberculosis","volume":"18","year":"2024","journal-title":"J. Biol. Dyn."},{"key":"2026062507374694500_c2","author":"World Health Organization"},{"key":"2026062507374694500_c3","doi-asserted-by":"publisher","first-page":"e228","DOI":"10.1016\/S1473-3099(18)30134-8","article-title":"Progression from latent infection to active disease in dynamic tuberculosis transmission models: A systematic review of the validity of modelling assumptions","volume":"18","year":"2018","journal-title":"Lancet Infect. Dis."},{"issue":"1944","key":"2026062507374694500_c4","doi-asserted-by":"publisher","first-page":"20201635","DOI":"10.1098\/rspb.2020.1635","article-title":"Self-clearance of Mycobacterium tuberculosis infection: Implications for lifetime risk and population at-risk of tuberculosis disease","volume":"288","year":"2021","journal-title":"Proc. R. Soc. B: Biol. Sci."},{"issue":"1","key":"2026062507374694500_c5","doi-asserted-by":"publisher","first-page":"111","DOI":"10.3934\/mbe.2012.9.111","article-title":"Threshold dynamics for a tuberculosis model with seasonality","volume":"9","year":"2011","journal-title":"Math. Biosci. Eng."},{"issue":"24","key":"2026062507374694500_c6","doi-asserted-by":"publisher","first-page":"2271","DOI":"10.1056\/NEJMcp2108501","article-title":"Latent tuberculosis infection","volume":"385","year":"2021","journal-title":"N. Engl. J. Med."},{"key":"2026062507374694500_c7","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1111\/odi.12390","article-title":"HI\u2013TB co-infection: Mechanisms that drive reactivation of Mycobacterium tuberculosis in HIV infection","volume":"22","year":"2016","journal-title":"Oral Dis."},{"issue":"4","key":"2026062507374694500_c8","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1002\/wsbm.131","article-title":"A multifaceted approach to modeling the immune response in tuberculosis","volume":"3","year":"2011","journal-title":"Wiley Interdiscip. Rev.: Syst. Biol. Med."},{"key":"2026062507374694500_c9","author":"Central TB Division"},{"key":"2026062507374694500_c10","author":"World Health Organization"},{"key":"2026062507374694500_c11","author":"World Health Organization"},{"issue":"772","key":"2026062507374694500_c12","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1098\/rspa.1927.0118","article-title":"A contribution to the mathematical theory of epidemics","volume":"115","year":"1927","journal-title":"Proc. R. Soc. London A"},{"key":"2026062507374694500_c13","first-page":"193","article-title":"Mathematical models in epidemiological studies. I. Application to the cholera epidemic in Bari in 1973","volume":"19","year":"1977","journal-title":"Ann. Sclavo"},{"issue":"1\u20132","key":"2026062507374694500_c14","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/0025-5564(78)90006-8","article-title":"A generalization of the Kermack\u2013McKendrick deterministic epidemic model","volume":"42","year":"1978","journal-title":"Math. Biosci."},{"issue":"1","key":"2026062507374694500_c15","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1016\/j.jmaa.2008.07.042","article-title":"Backward bifurcation of an epidemic model with saturated treatment function","volume":"348","year":"2008","journal-title":"J. Math. Anal. Appl."},{"issue":"4","key":"2026062507374694500_c16","doi-asserted-by":"publisher","first-page":"473","DOI":"10.3934\/dcdsb.2002.2.473","article-title":"Optimal control of treatments in a two-strain tuberculosis model","volume":"2","year":"2002","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"issue":"1","key":"2026062507374694500_c17","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.jtbi.2011.03.009","article-title":"A dynamic model for tuberculosis transmission and optimal treatment strategies in South Korea","volume":"279","year":"2011","journal-title":"J. Theor. Biol."},{"issue":"7","key":"2026062507374694500_c18","doi-asserted-by":"publisher","first-page":"1566","DOI":"10.1007\/s11538-014-9962-6","article-title":"Optimal tuberculosis prevention and control strategy from a mathematical model based on real data","volume":"76","year":"2014","journal-title":"Bull. Math. Biol."},{"key":"2026062507374694500_c19","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1016\/j.idm.2023.03.005","article-title":"Studying the efficacy of isolation as a control strategy and elimination of tuberculosis in India: A mathematical model","volume":"8","year":"2023","journal-title":"Infect. Dis. Model."},{"issue":"5\u20138","key":"2026062507374694500_c20","first-page":"231","article-title":"Optimal control of tuberculosis with exogenous reinfection","volume":"3","year":"2009","journal-title":"Appl. Math. Sci."},{"issue":"3","key":"2026062507374694500_c21","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/tpbi.2000.1451","article-title":"A model for tuberculosis with exogenous reinfection","volume":"57","year":"2000","journal-title":"Theor. Popul. Biol."},{"issue":"4","key":"2026062507374694500_c22","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1007\/s11071-010-9683-9","article-title":"Optimal control of the transmission dynamics of tuberculosis","volume":"61","year":"2010","journal-title":"Nonlinear Dyn."},{"issue":"2","key":"2026062507374694500_c23","doi-asserted-by":"publisher","first-page":"468","DOI":"10.1002\/oca.70071","article-title":"Modeling and optimal control of infectious diseases with information\u2019s impact on behavioural change and on vaccination under saturated medical environment and time delays in controls","volume":"47","year":"2026","journal-title":"Optim. Control Appl. Methods"},{"key":"2026062507374694500_c24","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s12591-019-00467-x","article-title":"Role of optimal screening and treatment on infectious diseases dynamics in presence of self-protection of susceptible","volume":"31","year":"2023","journal-title":"Differ. Equ. Dyn. Syst."},{"key":"2026062507374694500_c25","doi-asserted-by":"publisher","first-page":"123237","DOI":"10.1016\/j.physa.2019.123237","article-title":"Analysis of tuberculosis model with saturated incidence rate and optimal control","volume":"540","year":"2020","journal-title":"Physica A"},{"key":"2026062507374694500_c26","doi-asserted-by":"publisher","first-page":"1028","DOI":"10.1140\/epjp\/s13360-022-03201-9","article-title":"Nonlinear dynamics of a SIRI model incorporating the impact of information and saturated treatment with optimal control","volume":"137","year":"2022","journal-title":"Eur. Phys. J. Plus."},{"issue":"6","key":"2026062507374694500_c27","doi-asserted-by":"publisher","first-page":"2882","DOI":"10.1002\/oca.70035","article-title":"Modeling and optimal management of control policies for vector-borne diseases: A study of cost-effectiveness and policy impact","volume":"46","year":"2025","journal-title":"Optim. Control Appl. Methods"},{"issue":"6","key":"2026062507374694500_c28","doi-asserted-by":"publisher","first-page":"184","DOI":"10.3390\/diseases13060184","article-title":"Integration of AI and ML in tuberculosis (TB) management: From diagnosis to drug discovery","volume":"13","year":"2025","journal-title":"Diseases"},{"issue":"6","key":"2026062507374694500_c29","doi-asserted-by":"publisher","first-page":"1075","DOI":"10.3390\/diagnostics13061075","article-title":"Using an artificial intelligence approach to predict the adverse effects and prognosis of tuberculosis","volume":"13","year":"2023","journal-title":"Diagnostics"},{"key":"2026062507374694500_c30","doi-asserted-by":"publisher","first-page":"111988","DOI":"10.1016\/j.jtbi.2024.111988","article-title":"A comprehensive study on tuberculosis prediction models: Integrating machine learning into epidemiological analysis","volume":"597","year":"2025","journal-title":"J. Theor. Biol."},{"issue":"10","key":"2026062507374694500_c31","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/s10994-025-06848-4","article-title":"Epidemic-guided deep learning for spatiotemporal forecasting of tuberculosis outbreak","volume":"114","year":"2025","journal-title":"Mach. Learn."},{"key":"2026062507374694500_c32","doi-asserted-by":"publisher","first-page":"111225","DOI":"10.1016\/j.compbiomed.2025.111225","article-title":"Forecasting tuberculosis through mechanistic learning of transmission dynamics: Insights from a case study in India","volume":"198","year":"2025","journal-title":"Comput. Biol. Med."},{"issue":"11","key":"2026062507374694500_c33","doi-asserted-by":"publisher","first-page":"113118","DOI":"10.1063\/5.0299032","article-title":"Threshold dynamics and epidemic-informed machine learning for forecasting of Mpox: A US case study","volume":"35","year":"2025","journal-title":"Chaos"},{"key":"2026062507374694500_c34","doi-asserted-by":"publisher","first-page":"100060","DOI":"10.1016\/j.nls.2025.100060","article-title":"A deep learning approach to model and predict tuberculosis in both diabetic smoker and non-smoker individuals using Physics-Informed Neural Networks","volume":"5","year":"2025","journal-title":"Nonlinear Sci."},{"issue":"10","key":"2026062507374694500_c35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pone.0309151","article-title":"Machine learning algorithms to predict treatment success for patients with pulmonary tuberculosis","volume":"19","year":"2024","journal-title":"PLoS One"},{"issue":"6","key":"2026062507374694500_c36","doi-asserted-by":"publisher","first-page":"184","DOI":"10.3390\/diseases13060184","article-title":"Integration of AI and ML in tuberculosis (TB) management: From diagnosis to drug discovery","volume":"13","year":"2025","journal-title":"Diseases"},{"key":"2026062507374694500_c37","doi-asserted-by":"publisher","first-page":"S92","DOI":"10.1016\/j.ijtb.2025.11.012","article-title":"Multi-modal AI approach for early tuberculosis detection by combining symptom, imaging, and clinical data","volume":"72","year":"2025","journal-title":"Indian J. Tuberc."},{"key":"2026062507374694500_c38","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/BF00277162","article-title":"Dynamical behaviour of epidemiological models with nonlinear incidence rates","volume":"25","year":"1987","journal-title":"J. Math. Biol."},{"issue":"1\u20132","key":"2026062507374694500_c39","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S0378-4754(02)00002-2","article-title":"Global stability of a two-stage epidemic model with generalized non-linear incidence","volume":"60","year":"2002","journal-title":"Math. Comput. Simul."},{"issue":"2\u20133","key":"2026062507374694500_c40","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1016\/S0096-3003(02)00372-7","article-title":"A qualitative study of a vaccination model with non-linear incidence","volume":"143","year":"2003","journal-title":"Appl. Math. Comput."},{"key":"2026062507374694500_c41","volume-title":"Mathematical Biology","year":"1998"},{"key":"2026062507374694500_c42","author":"The World Bank"},{"key":"2026062507374694500_c43","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1140\/epjp\/s13360-025-05978-x","article-title":"Effective strategies toward controlling tuberculosis: Optimal control and cost-effectiveness analysis","volume":"140","year":"2025","journal-title":"Eur. Phys. J. Plus"},{"issue":"2","key":"2026062507374694500_c44","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/j.jtbi.2008.05.015","article-title":"Saturation recovery leads to multiple endemic equilibria and backward bifurcation","volume":"254","year":"2008","journal-title":"J. Theor. Biol."},{"issue":"11","key":"2026062507374694500_c45","doi-asserted-by":"publisher","first-page":"4438","DOI":"10.1016\/j.cnsns.2011.03.026","article-title":"Analysis of stability and bifurcation for an SEIR epidemic model with saturated recovery rate","volume":"16","year":"2011","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"1","key":"2026062507374694500_c46","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","article-title":"Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission","volume":"180","year":"2002","journal-title":"Math. Biosci."},{"issue":"47","key":"2026062507374694500_c47","doi-asserted-by":"publisher","first-page":"873","DOI":"10.1098\/rsif.2009.0386","article-title":"The construction of next-generation matrices for compartmental epidemic models","volume":"7","year":"2010","journal-title":"J. R. Soc. Interface"},{"key":"2026062507374694500_c48","doi-asserted-by":"publisher","first-page":"115899","DOI":"10.1016\/j.chaos.2024.115899","article-title":"Modeling HIV\/AIDS with the effect of screening in India: A stochastic sex-structured approach incorporating logarithmic mean-reverting Ornstein\u2013Uhlenbeck process","volume":"191","year":"2025","journal-title":"Chaos Soliton. Fract."},{"key":"2026062507374694500_c49","doi-asserted-by":"publisher","first-page":"113775","DOI":"10.1016\/j.chaos.2023.113775","article-title":"Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments","volume":"174","year":"2023","journal-title":"Chaos Soliton. Fract."},{"issue":"3","key":"2026062507374694500_c50","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1016\/j.idm.2017.08.001","article-title":"Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts","volume":"2","year":"2017","journal-title":"Infect. Dis. Model."},{"key":"2026062507374694500_c51","author":"The World Bank"},{"issue":"3-4","key":"2026062507374694500_c52","doi-asserted-by":"publisher","first-page":"62","DOI":"10.14745\/ccdr.v43i34a01","article-title":"Latent tuberculosis infection: An overview","volume":"43","year":"2017","journal-title":"Can. Commun. Dis. Rep."},{"key":"2026062507374694500_c53","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.jtbi.2014.05.023","article-title":"Construction of a mathematical model for tuberculosis transmission in highly endemic regions of the Asia-Pacific","volume":"358","year":"2014","journal-title":"J. Theor. Biol."},{"key":"2026062507374694500_c54","doi-asserted-by":"publisher","first-page":"100341","DOI":"10.1016\/j.health.2024.100341","article-title":"A deterministic compartment model for analyzing tuberculosis dynamics considering vaccination and reinfection","volume":"5","year":"2024","journal-title":"Healthc. Anal."},{"issue":"4","key":"2026062507374694500_c55","doi-asserted-by":"publisher","first-page":"e17601","DOI":"10.1371\/journal.pone.0017601","article-title":"Natural history of tuberculosis: Duration and fatality of untreated pulmonary tuberculosis in HIV negative patients: A systematic review","volume":"6","year":"2011","journal-title":"PLoS One"},{"key":"2026062507374694500_c56","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.chaos.2010.09.002","article-title":"Global stability of two models with incomplete treatment for tuberculosis","volume":"43","year":"2010","journal-title":"Chaos Soliton. Fract."},{"key":"2026062507374694500_c57","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s12190-025-02659-x","article-title":"Mathematical modeling of tuberculosis transmission dynamics: Assessing vaccination impact with environmental transmission and reinfection","volume":"72","year":"2026","journal-title":"J. Appl. Math. Comput."},{"issue":"4","key":"2026062507374694500_c58","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pone.0230964","article-title":"Country-specific intervention strategies for top three TB burden countries using mathematical model","volume":"15","year":"2020","journal-title":"PLoS One"},{"issue":"2","key":"2026062507374694500_c59","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1016\/j.mbs.2013.05.005","article-title":"Optimal control for a tuberculosis model with reinfection and post-exposure interventions","volume":"244","year":"2013","journal-title":"Math. Biosci."},{"key":"2026062507374694500_c60","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1016\/j.jtbi.2018.01.026","article-title":"Mathematical model and intervention strategies for mitigating tuberculosis in the Philippines","volume":"443","year":"2018","journal-title":"J. Theor. Biol."},{"key":"2026062507374694500_c61","volume-title":"The Mathematical Theory of Optimal Processes","year":"1962"},{"key":"2026062507374694500_c62","volume-title":"Deterministic and Stochastic Optimal Control","year":"1975"},{"key":"2026062507374694500_c63","volume-title":"Optimal Control Applied to Biological Models","year":"2007"},{"issue":"1","key":"2026062507374694500_c64","doi-asserted-by":"publisher","first-page":"971","DOI":"10.1007\/s11071-021-06607-9","article-title":"Global dynamics and control strategies of an epidemic model having logistic growth, non-monotone incidence with the impact of limited hospital beds","volume":"105","year":"2021","journal-title":"Nonlinear Dyn."},{"key":"2026062507374694500_c65","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/j.orhc.2017.08.004","article-title":"Optimal control of intervention strategies and cost effectiveness analysis for a Zika virus model","volume":"18","year":"2018","journal-title":"Oper. Res. Health Care"},{"key":"2026062507374694500_c66","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/j.amc.2019.04.02","article-title":"Optimal control and cost-effectiveness analysis of a Zika virus infection model with comprehensive interventions","volume":"359","year":"2019","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"2026062507374694500_c67","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.biosystems.2012.09.008","article-title":"Optimal control strategies and cost-effectiveness analysis of a malaria model","volume":"111","year":"2013","journal-title":"BioSystems"},{"issue":"1","key":"2026062507374694500_c68","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s40435-022-00969-7","article-title":"Complex dynamics and control analysis of an epidemic model with non-monotone incidence and saturated treatment","volume":"11","year":"2023","journal-title":"Int. J. Dyn. Control"},{"issue":"4","key":"2026062507374694500_c69","doi-asserted-by":"publisher","first-page":"3893","DOI":"10.1007\/s11071-022-07777-w","article-title":"Mathematical modeling for COVID-19 with focus on intervention strategies and cost-effectiveness analysis","volume":"110","year":"2022","journal-title":"Nonlinear Dyn."},{"issue":"2","key":"2026062507374694500_c70","doi-asserted-by":"publisher","first-page":"e0171102","DOI":"10.1371\/journal.pone.0171102","article-title":"Optimal control and cost-effective analysis of malaria\/visceral leishmaniasis co-infection","volume":"12","year":"2017","journal-title":"PLoS One"},{"key":"2026062507374694500_c71","doi-asserted-by":"publisher","first-page":"103889","DOI":"10.1016\/j.rinp.2021.103889","article-title":"Non-seasonal and seasonal relapse model for Q fever disease with comprehensive cost-effectiveness analysis","volume":"22","year":"2021","journal-title":"Results Phys."},{"key":"2026062507374694500_c72","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/s40314-025-03543-x","article-title":"Impact of media awareness, treatment saturation, and LTBI control on tuberculosis transmission: A mathematical modeling approach","volume":"45","year":"2026","journal-title":"Comput. Appl. Math."}],"container-title":["Chaos: An Interdisciplinary Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0332974\/21055736\/063144_1_5.0332974.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0332974\/21055736\/063144_1_5.0332974.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T11:37:57Z","timestamp":1782387477000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/cha\/article\/36\/6\/063144\/3396652\/A-data-driven-tuberculosis-model-with-behavioral"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,1]]},"references-count":72,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,6,1]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0332974","relation":{},"ISSN":["1054-1500","1089-7682"],"issn-type":[{"value":"1054-1500","type":"print"},{"value":"1089-7682","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,6]]},"published":{"date-parts":[[2026,6,1]]},"article-number":"063144"}}