Stability analysis of mathematical model for the dynamics of diabetes mellitus and its complications in a population
DOI:
https://doi.org/10.15282/daam.v3i1.7192Keywords:
Diabetes mellitus, Complications, Mathematical model, Stability analysisAbstract
This study present a mathematical model for the dynamics of diabetess and its complications in a population. The population under study was compartmentalized into healthy, susceptible, diabetic without complications, diabetic with complication and diabetic with complications undergoing treatment. The model is a system of linear ordinary differential equations. The stability of the model was investigated using Bellman and Coke method and the system was found to be stable.
References
Diabetes basics [Internet]. International Diabetes Federation. Available from: https://idf.org/about-diabetes/what-is-diabetes/
Organization WH. Diabetes Action Now: an initiative of the World Health Organization and the International Diabetes Federation [Internet]. iris.who.int. World Health Organization; 2004 [cited 2024 Apr 3]. Available from: https://iris.who.int/handle/10665/42934
World Health Organization. Diabetes [Internet]. World Health Organisation. 2023. Available from: https://www.who.int/news-room/fact-sheets/detail/diabetes
Gregg EW, Sattar N, Ali MK. The changing face of diabetes complications. The lancet Diabetes & endocrinology. 2016 Jun 1;4(6):537-47.
Gregg EW, Cheng YJ, Saydah S, Cowie C, Garfield S, Geiss L, Barker L. Trends in death rates among US adults with and without diabetes between 1997 and 2006: findings from the National Health Interview Survey. Diabetes care. 2012 Jun 1;35(6):1252-7.
Giovannucci E, Harlan DM, Archer MC, Bergenstal RM, Gapstur SM, Habel LA, Pollak M, Regensteiner JG, Yee D. Diabetes and cancer: a consensus report. CA: a cancer journal for clinicians. 2010 Jul;60(4):207-21.
Dooley KE, Chaisson RE. Tuberculosis and diabetes mellitus: convergence of two epidemics. The Lancet infectious diseases. 2009 Dec 1;9(12):737-46.
Magee MJ, Blumberg HM, Narayan KV. Commentary: Co-occurrence of tuberculosis and diabetes: new paradigm of epidemiological transition. International Journal of Epidemiology. 2011 Apr 1;40(2):428-31.
Ali MK, Bullard KM, Gregg EW, Del Rio C. A cascade of care for diabetes in the United States: visualizing the gaps. Annals of internal medicine. 2014 Nov 18;161(10):681-9.
Ali MK, Jaacks LM, Kowalski AJ, Siegel KR, Ezzati M. Noncommunicable diseases: three decades of global data show a mixture of increases and decreases in mortality rates. Health affairs. 2015 Sep 1;34(9):1444-55.
Danaei G, Lawes CM, Vander Hoorn S, Murray CJ, Ezzati M. Global and regional mortality from ischaemic heart disease and stroke attributable to higher-than-optimum blood glucose concentration: comparative risk assessment. The Lancet. 2006 Nov 11;368(9548):1651-9.
Home, Resources, diabetes L with, Acknowledgement, FAQs, Contact, et al. 7th edition | IDF Diabetes Atlas [Internet]. 2015. Available from: https://diabetesatlas.org/atlas/seventh-edition/
Roglic G, Unwin N, Bennett PH, Mathers C, Tuomilehto J, Nag S, Connolly V, King H. The burden of mortality attributable to diabetes: realistic estimates for the year 2000. Diabetes care. 2005 Sep 1;28(9):2130-5.
Boutayeb A, Twizell EH, Achouayb K, Chetouani A. A mathematical model for the burden of diabetes and its complications. Biomedical engineering online. 2004 Dec;3:1-8.
Permatasari AH, Tjahjana RH, Udjiani T. Global stability for linear system and controllability for nonlinear system in the dynamics model of diabetics population. InJournal of Physics: Conference Series 2018 May 1 (Vol. 1025, No. 1, p. 012086). IOP Publishing.
Widyaningsih P, Affan RC, Saputro DR. A mathematical model for the epidemiology of diabetes mellitus with lifestyle and genetic factors. In Journal of physics: conference series 2018 Jun 1 (Vol. 1028, p. 012110). IOP Publishing.
Kumar SD, Pandit P. An ordinary differential equation model of diabetic population in New Delhi. Indian Journal of Mathematics and Mathematical Sciences. 2011;7:45-50.
Akinsola VO, Oluyo TO. Mathematical model of the complications and control of diabetes mellitus. International Journal of Mathematics and Computer Applications Research (UMCAR). 2014 Oct;4(5):1-4.
Adamu I, Momoh A, Tahir A. Stability analysis of the mathematical model for the dynamics of diabetic population under the combine effect of birth rate and treatment. International Journal of Science and Technology. 2016;5(1):26-35.
Bellmann RE, Cooke KL. Differential-difference Equations: A Report Prepared for US Air Force Project Rand. Rand Corporation; 1963.
Aye PO, Akinwande NI, Kuta FA, Kayode DJ. Analytical Solution of a Mathematical Model for the Dynamics of Diabetes Mellitus and Its Complications incorporating Treatment and Positive Lifestyle as Control. Science Research Annals. 2019; 67 - 76
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