{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,27]],"date-time":"2026-10-27T07:37:10Z","timestamp":1793086630890,"version":"4.5.0"},"reference-count":49,"publisher":"SAGE Publications","issue":"10","license":[{"start":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T00:00:00Z","timestamp":1790208000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Proc Inst Mech Eng H"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:p>A mathematical model of Type 2 Diabetes Mellitus is developed in this paper, by which the dynamics of the disease can be predicted with the aid of the related extracted ordinary differential equations. The important biological factors, including physical activities and insulin sensitivity, are considered in modeling the disease. Unlike previous models that mainly focused on type 1 diabetes or simplified Bergman-based approaches, the proposed model takes into account the complex dynamics of type 2 diabetes and enables the simultaneous regulation of glucose and insulin effectiveness using two controlling inputs. Also, an efficient control strategy based on a Sliding Mode Controller (SMC) is designed and implemented on the extracted model. This controller is a robust, nonlinear, and closed-loop compensator by which the glucose level of the blood can be stabilized effectively. This controller is able to customize the therapy for type 2 diabetes and provide a framework that can help physicians personalize the treatment regimens based on each individual\u2019s insulin sensitivity. With the aid of some simulation scenarios in MATLAB, the accuracy and correctness of the proposed model are shown. Also, the efficiency of the designed controller in managing the glucose level of the blood is verified by conducting some comparative and analytical simulations. Results confirm that the developed framework enables both reliable monitoring and successful regulation of glucose levels in the presence of diverse biological influences.<\/jats:p>","DOI":"10.1177\/09544119261490966","type":"journal-article","created":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T11:16:19Z","timestamp":1790248579000},"page":"1066-1083","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Mathematical model development of type 2 diabetes mellitus considering insulin sensitivity and control of glucose using sliding mode approach"],"prefix":"10.1177","volume":"240","author":[{"given":"Danial","family":"Kiaei","sequence":"first","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Guilan, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4083-6470","authenticated-orcid":false,"given":"Hami","family":"Tourajizadeh","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Kharazmi University, Tehran, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2791-6591","authenticated-orcid":false,"given":"Behnam","family":"Miripour Fard","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Guilan, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2026,9,24]]},"reference":[{"key":"e_1_3_4_2_2","doi-asserted-by":"crossref","unstructured":"Pan L Sun W Wan W et al. Research progress of diabetic disease prediction model in deep learning. J Theory Pract Eng Sci 2023; 3: 15\u201321. https:\/\/doi.org\/10.53469\/jtpes.2023.03(12).03","DOI":"10.53469\/jtpes.2023.03(12).03"},{"key":"e_1_3_4_3_2","doi-asserted-by":"crossref","unstructured":"Dubey RS Goswami P. Mathematical model of diabetes and its complication involving fractional operator without singular kernal. Discrete Contin Dyn Syst Ser S 2021; 14: 2151\u20132161. https:\/\/doi.org\/10.3934\/dcdss.2020144","DOI":"10.3934\/dcdss.2020144"},{"key":"e_1_3_4_4_2","doi-asserted-by":"crossref","unstructured":"Al-Taee MA Al-Nuaimy W Muhsin ZJ et al. Robot assistant in management of diabetes in children based on the internet of things. IEEE Internet Things J 2017; 4: 437\u2013445. https:\/\/doi.org\/10.1109\/jiot.2016.2623767","DOI":"10.1109\/JIOT.2016.2623767"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1186\/1475-925X-3-20"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/RBME.2009.2036073"},{"key":"e_1_3_4_7_2","doi-asserted-by":"crossref","unstructured":"Srivastava HM Shanker Dubey R Jain M. A study of the fractional-order mathematical model of diabetes and its resulting complications. Math Methods Appl Sci 2019; 42: 4570\u20134583. https:\/\/doi.org\/10.1002\/mma.5681","DOI":"10.1002\/mma.5681"},{"key":"e_1_3_4_8_2","doi-asserted-by":"crossref","unstructured":"Skovs\u00f8 S. Modeling type 2 diabetes in rats using high fat diet and streptozotocin. J Diabetes Invest 2014; 5: 349\u2013358. https:\/\/doi.org\/10.1111\/jdi.12235","DOI":"10.1111\/jdi.12235"},{"key":"e_1_3_4_9_2","doi-asserted-by":"crossref","unstructured":"Contreras I Vehi J. Artificial intelligence for diabetes management and decision support: literature review. J Med Internet Res 2018; 20: e10775. https:\/\/doi.org\/10.2196\/10775","DOI":"10.2196\/10775"},{"key":"e_1_3_4_10_2","doi-asserted-by":"crossref","unstructured":"Farmaki P Damaskos C Garmpis N et al. Complications of the Type 2 diabetes mellitus. Curr Cardiol Rev 2020; 16: 249\u2013251. https:\/\/doi.org\/10.2174\/1573403X1604201229115531","DOI":"10.2174\/1573403X1604201229115531"},{"key":"e_1_3_4_11_2","doi-asserted-by":"crossref","unstructured":"De Gaetano A Hardy T Beck B et al. Mathematical models of diabetes progression. Am J Physiol Endocrinol Metab 2008; 295: E1462\u2013E1479. https:\/\/doi.org\/10.1152\/ajpendo.90444.2008","DOI":"10.1152\/ajpendo.90444.2008"},{"key":"e_1_3_4_12_2","doi-asserted-by":"crossref","unstructured":"Kovatchev B. Automated closed-loop control of diabetes: the artificial pancreas. Bioelectron Med 2018; 4: 14. https:\/\/doi.org\/10.1186\/s42234-018-0015-6","DOI":"10.1186\/s42234-018-0015-6"},{"key":"e_1_3_4_13_2","doi-asserted-by":"crossref","unstructured":"Svane J Pedersen-Bjergaard U Tfelt-Hansen J. Diabetes and the risk of sudden cardiac death. Curr Cardiol Rep 2020; 22: 112. https:\/\/doi.org\/10.1007\/s11886-020-01366-2","DOI":"10.1007\/s11886-020-01366-2"},{"key":"e_1_3_4_14_2","doi-asserted-by":"crossref","unstructured":"Siscovick DS Sotoodehnia N Rea TD et al. Type 2 diabetes mellitus and the risk of sudden cardiac arrest in the community. Rev Endocr Metab Disord 2010; 11: 53\u201359. https:\/\/doi.org\/10.1007\/s11154-010-9133-5","DOI":"10.1007\/s11154-010-9133-5"},{"key":"e_1_3_4_15_2","doi-asserted-by":"crossref","unstructured":"Singh KB Nnadozie MC Abdal M et al. Type 2 diabetes and causes of sudden cardiac death: a systematic review. Cureus 2021; 13: 9. https:\/\/doi.org\/10.7759\/cureus.18145","DOI":"10.7759\/cureus.18145"},{"key":"e_1_3_4_16_2","doi-asserted-by":"crossref","unstructured":"Bhatwadekar AD Shughoury A Belamkar A et al. Genetics of diabetic retinopathy a leading cause of irreversible blindness in the industrialized world. Genes 2021; 12: 1200. https:\/\/doi.org\/10.3390\/genes12081200","DOI":"10.3390\/genes12081200"},{"key":"e_1_3_4_17_2","doi-asserted-by":"crossref","unstructured":"Kropp M Golubnitschaja O Mazurakova A et al. Diabetic retinopathy as the leading cause of blindness and early predictor of cascading complications\u2014risks and mitigation. EPMA J 2023; 14: 21\u201342. https:\/\/doi.org\/10.1007\/s13167-023-00314-8","DOI":"10.1007\/s13167-023-00314-8"},{"key":"e_1_3_4_18_2","doi-asserted-by":"crossref","unstructured":"Lu Y Wang W Liu J et al. Vascular complications of diabetes: a narrative review. Medicine 2023; 102: e35285. https:\/\/doi.org\/10.1097\/MD.0000000000035285","DOI":"10.1097\/MD.0000000000035285"},{"key":"e_1_3_4_19_2","first-page":"294","volume-title":"Diabetic eye disease\u2014from therapeutic pipeline to the real world","author":"Gonzalez-Cortes JH","year":"2021","unstructured":"Gonzalez-Cortes JH, Gonzalez-Cantu JE, Sudhalkar A, et al. Treatment algorithm in proliferative diabetic retinopathy\u2014from protocols to the real world. In: Diabetic eye disease\u2014from therapeutic pipeline to the real world. London, IntechOpen, 2021, p. 294."},{"key":"e_1_3_4_20_2","doi-asserted-by":"crossref","unstructured":"Kiaei D Tourajizadeh H. Modeling of cancer growth considering the dynamics of mutation and controlling the cell proliferation of cancer in the presence of mutation using adaptive control. Int J Biomath 2025; 4: 2550043. https:\/\/doi.org\/10.1142\/s1793524525500433","DOI":"10.1142\/S1793524525500433"},{"key":"e_1_3_4_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/IKT57960.2022.10039006"},{"key":"e_1_3_4_22_2","doi-asserted-by":"crossref","unstructured":"Tourajizadeh H Farbodi Z Kiaei D et al. Numerical modelling and control of tumour mutation using piecewise fuzzy approach. Lat Am Appl Res 2025; 55: 123\u2013135. https:\/\/doi.org\/10.52292\/j.laar.2025.3476","DOI":"10.52292\/j.laar.2025.3476"},{"key":"e_1_3_4_23_2","doi-asserted-by":"crossref","unstructured":"Tourajizadeh H G Zarandi Z Kiaei D et al. Dynamic modelling and robust control of cancer mutation employing sliding mode based chemotherapy. Sci Iran 2024; 0: 0\u20130. https:\/\/doi.org\/10.24200\/sci.2024.62871.8072","DOI":"10.24200\/sci.2024.62871.8072"},{"key":"e_1_3_4_24_2","doi-asserted-by":"crossref","unstructured":"Ghaffari Laleh N Loeffler CML Grajek J et al. Classical mathematical models for prediction of response to chemotherapy and immunotherapy. PLoS Comput Biol 2022; 18: e1009822. https:\/\/doi.org\/10.1371\/journal.pcbi.1009822","DOI":"10.1371\/journal.pcbi.1009822"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1186\/1475-925X-5-43"},{"key":"e_1_3_4_26_2","doi-asserted-by":"crossref","unstructured":"Kouidere A Labzai A Ferjouchia H et al. A new mathematical modeling with optimal control strategy for the dynamics of population of diabetics and its complications with effect of behavioral factors. J Appl Math 2020; 2020: 1\u201312. https:\/\/doi.org\/10.1155\/2020\/1943410","DOI":"10.1155\/2020\/1943410"},{"key":"e_1_3_4_27_2","doi-asserted-by":"crossref","unstructured":"Nath A Biradar S Balan A et al. Physiological models and control for type 1 diabetes mellitus: a brief review. IFAC-PapersOnLine 2018; 51: 289\u2013294. https:\/\/doi.org\/10.1016\/j.ifacol.2018.05.077","DOI":"10.1016\/j.ifacol.2018.05.077"},{"key":"e_1_3_4_28_2","doi-asserted-by":"crossref","unstructured":"De Nicolao G Magni L Man CD et al. Modeling and control of diabetes: towards the artificial pancreas. IFAC Proc Volumes 2011; 44: 7092\u20137101. https:\/\/doi.org\/10.3182\/20110828-6-it-1002.03036","DOI":"10.3182\/20110828-6-IT-1002.03036"},{"key":"e_1_3_4_29_2","doi-asserted-by":"crossref","unstructured":"Khan FA Zeb K Al-Rakhami M et al. Detection and prediction of diabetes using data mining: a comprehensive review. IEEE Access 2021; 9: 43711\u201343735. https:\/\/doi.org\/10.1109\/access.2021.3059343","DOI":"10.1109\/ACCESS.2021.3059343"},{"key":"e_1_3_4_30_2","doi-asserted-by":"crossref","unstructured":"Resalat N Hilts W Youssef JE et al. Adaptive control of an artificial pancreas using model identification adaptive postprandial insulin delivery and heart rate and accelerometry as control inputs. J Diabetes Sci Technol 2019; 13: 1044\u20131053. https:\/\/doi.org\/10.1177\/1932296819881467","DOI":"10.1177\/1932296819881467"},{"key":"e_1_3_4_31_2","doi-asserted-by":"crossref","unstructured":"Turksoy K Cinar A. Adaptive control of artificial pancreas systems - a review. J Healthc Eng 2014; 5(1): 1\u201322. https:\/\/doi.org\/10.1260\/2040-2295.5.1.1","DOI":"10.1260\/2040-2295.5.1.1"},{"key":"e_1_3_4_32_2","doi-asserted-by":"crossref","unstructured":"Taherinasab S Soleimaniasl S Taherinasab S. Application of model reference adaptive control and modified Smith predictor to control blood glucose in type 1 diabetic patients. Math Comput Simul 2022; 194: 198\u2013209. https:\/\/doi.org\/10.1016\/j.matcom.2021.05.033","DOI":"10.1016\/j.matcom.2021.05.033"},{"key":"e_1_3_4_33_2","doi-asserted-by":"crossref","unstructured":"Ahmad S Ahmed N Ilyas M et al. Super twisting sliding mode control algorithm for developing artificial pancreas in type 1 diabetes patients. Biomed Signal Process Control 2017; 38: 200\u2013211. https:\/\/doi.org\/10.1016\/j.bspc.2017.06.009","DOI":"10.1016\/j.bspc.2017.06.009"},{"key":"e_1_3_4_34_2","doi-asserted-by":"crossref","unstructured":"Shao K. Adaptive tracking control of a magnetic levitation system based on class K\u221e function. Eur J Control 2024; 76: 100963. https:\/\/doi.org\/10.1016\/j.ejcon.2024.100963","DOI":"10.1016\/j.ejcon.2024.100963"},{"key":"e_1_3_4_35_2","doi-asserted-by":"crossref","unstructured":"Xavier J Divya N Krithiga MB et al. Blood glucose regulation in type-1 diabetic patients using sliding mode control based on nonlinear transformation. IFAC-PapersOnLine 2022; 55: 902\u2013907. https:\/\/doi.org\/10.1016\/j.ifacol.2022.04.148","DOI":"10.1016\/j.ifacol.2022.04.148"},{"key":"e_1_3_4_36_2","doi-asserted-by":"crossref","unstructured":"Rsetam K Cao Z Man Z et al. GPIO-based continuous sliding mode control for networked control systems under communication delays with experiments on servo motors. IEEE\/CAA J Autom Sin 2025; 12: 99\u2013113. https:\/\/doi.org\/10.1109\/jas.2024.124812","DOI":"10.1109\/JAS.2024.124812"},{"key":"e_1_3_4_37_2","doi-asserted-by":"crossref","unstructured":"Ali K Cao Z Rsetam K et al. Practical adaptive fast terminal sliding mode control for servo motors. Actuators 2023; 12: 433. https:\/\/doi.org\/10.3390\/act12120433","DOI":"10.3390\/act12120433"},{"key":"e_1_3_4_38_2","doi-asserted-by":"crossref","unstructured":"Ali K Cao Z Rsetam K et al. Robust adaptive integral fast sliding mode control for servo motors. Mechatronics 2026; 117: 103504. https:\/\/doi.org\/10.1016\/j.mechatronics.2026.103504","DOI":"10.1016\/j.mechatronics.2026.103504"},{"key":"e_1_3_4_39_2","doi-asserted-by":"crossref","unstructured":"Mongini PA Ragni M Magni L et al. Periodic MPC for glucose control in type 1 diabetes. IFAC-PapersOnLine 2025; 59: 25\u201330. https:\/\/doi.org\/10.1016\/j.ifacol.2025.06.005","DOI":"10.1016\/j.ifacol.2025.06.005"},{"key":"e_1_3_4_40_2","doi-asserted-by":"crossref","unstructured":"Toffanin C Magni L. Personalized constrained MPC for glucose regulation. IFAC-PapersOnLine 2023; 56: 9648\u20139653. https:\/\/doi.org\/10.1016\/j.ifacol.2023.10.272","DOI":"10.1016\/j.ifacol.2023.10.272"},{"key":"e_1_3_4_41_2","doi-asserted-by":"crossref","unstructured":"Borri A Pola G Pepe P et al. Symbolic control design of an artificial pancreas for type-2 diabetes. IEEE Trans Control Syst Technol 2022; 30: 2131\u20132146. https:\/\/doi.org\/10.1109\/tcst.2021.3135320","DOI":"10.1109\/TCST.2021.3135320"},{"key":"e_1_3_4_42_2","doi-asserted-by":"publisher","DOI":"10.1109\/BMEI.2015.7401518"},{"key":"e_1_3_4_43_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10928-006-9008-2"},{"key":"e_1_3_4_44_2","volume-title":"Applied nonlinear control","author":"Slotine JJE","year":"1991","unstructured":"Slotine JJE, Li W. Applied nonlinear control. Prentice Hall, 1991."},{"key":"e_1_3_4_45_2","doi-asserted-by":"crossref","unstructured":"Satirapoj B Watanakijthavonkul K Supasyndh O. Safety and efficacy of low dose pioglitazone compared with standard dose pioglitazone in type 2 diabetes with chronic kidney disease: a randomized controlled trial. PLoS One 2018; 13: e0206722. https:\/\/doi.org\/10.1371\/journal.pone.0206722","DOI":"10.1371\/journal.pone.0206722"},{"key":"e_1_3_4_46_2","doi-asserted-by":"publisher","DOI":"10.2337\/diacare.23.11.1605"},{"key":"e_1_3_4_47_2","doi-asserted-by":"publisher","DOI":"10.2337\/diacare.25.3.517"},{"key":"e_1_3_4_48_2","volume-title":"10th Mediterranean conference on control and automation (MED2002)","author":"Tokat S","unstructured":"Tokat S, Eksin I, Guzelkaya M. Sliding mode control using a nonlinear time-varying sliding surface. In: 10th Mediterranean conference on control and automation (MED2002), Lisbon, Portugal, 9 July 2002."},{"key":"e_1_3_4_49_2","doi-asserted-by":"crossref","unstructured":"Antuna-Puente B Disse E Rabasa-Lhoret R et al. How can we measure insulin sensitivity\/resistance? Diabetes Metab 2011; 37: 179\u2013188. https:\/\/doi.org\/10.1016\/j.diabet.2011.01.002","DOI":"10.1016\/j.diabet.2011.01.002"},{"key":"e_1_3_4_50_2","doi-asserted-by":"crossref","unstructured":"Wang YF Khan M van den Berg HA. Interaction of fast and slow dynamics in endocrine control systems with an application to \u03b2-cell dynamics. Math Biosci 2012; 235: 8\u201318. https:\/\/doi.org\/10.1016\/j.mbs.2011.10.003","DOI":"10.1016\/j.mbs.2011.10.003"}],"container-title":["Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/09544119261490966","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/09544119261490966","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/09544119261490966","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,27]],"date-time":"2026-10-27T07:15:55Z","timestamp":1793085355000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/09544119261490966"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,24]]},"references-count":49,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2026,10]]}},"alternative-id":["10.1177\/09544119261490966"],"URL":"https:\/\/doi.org\/10.1177\/09544119261490966","relation":{},"ISSN":["0954-4119","2041-3033"],"issn-type":[{"value":"0954-4119","type":"print"},{"value":"2041-3033","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,24]]}}}