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Mathematical models of subcutaneous injection of insulin analogues: A mini-review
1. | Department of Mathematics, University of Louisville, Louisville, KY 40292, United States |
2. | Department of Cellular and Physiological Sciences; Department of Surgery, University of British Columbia, Vancouver, BC, Canada |
[1] |
Jiaxu Li, Yang Kuang. Systemically modeling the dynamics of plasma insulin in subcutaneous injection of insulin analogues for type 1 diabetes. Mathematical Biosciences & Engineering, 2009, 6 (1) : 41-58. doi: 10.3934/mbe.2009.6.41 |
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Peter W. Bates, Yu Liang, Alexander W. Shingleton. Growth regulation and the insulin signaling pathway. Networks and Heterogeneous Media, 2013, 8 (1) : 65-78. doi: 10.3934/nhm.2013.8.65 |
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Pasquale Palumbo, Simona Panunzi, Andrea De Gaetano. Qualitative behavior of a family of delay-differential models of the Glucose-Insulin system. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 399-424. doi: 10.3934/dcdsb.2007.7.399 |
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Saloni Rathee, Nilam. Quantitative analysis of time delays of glucose - insulin dynamics using artificial pancreas. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3115-3129. doi: 10.3934/dcdsb.2015.20.3115 |
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Jiaxu Li, Yang Kuang, Bingtuan Li. Analysis of IVGTT glucose-insulin interaction models with time delay. Discrete and Continuous Dynamical Systems - B, 2001, 1 (1) : 103-124. doi: 10.3934/dcdsb.2001.1.103 |
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Massimo Barnabei, Alessandro Borri, Andrea De Gaetano, Costanzo Manes, Pasquale Palumbo, Jorge Guerra Pires. A short-term food intake model involving glucose, insulin and ghrelin. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 1913-1926. doi: 10.3934/dcdsb.2021114 |
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J.W. Bruce, F. Tari. Generic 1-parameter families of binary differential equations of Morse type. Discrete and Continuous Dynamical Systems, 1997, 3 (1) : 79-90. doi: 10.3934/dcds.1997.3.79 |
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Patrick Nelson, Noah Smith, Stanca Ciupe, Weiping Zou, Gilbert S. Omenn, Massimo Pietropaolo. Modeling dynamic changes in type 1 diabetes progression: Quantifying $\beta$-cell variation after the appearance of islet-specific autoimmune responses. Mathematical Biosciences & Engineering, 2009, 6 (4) : 753-778. doi: 10.3934/mbe.2009.6.753 |
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Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch. Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure. Networks and Heterogeneous Media, 2021, 16 (2) : 283-315. doi: 10.3934/nhm.2021007 |
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Eduardo Liz, Manuel Pinto, Gonzalo Robledo, Sergei Trofimchuk, Victor Tkachenko. Wright type delay differential equations with negative Schwarzian. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 309-321. doi: 10.3934/dcds.2003.9.309 |
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Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. II. Convergence of the method of finite differences. Inverse Problems and Imaging, 2016, 10 (4) : 869-898. doi: 10.3934/ipi.2016025 |
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Jean Ginibre, Giorgio Velo. Modified wave operators without loss of regularity for some long range Hartree equations. II. Communications on Pure and Applied Analysis, 2015, 14 (4) : 1357-1376. doi: 10.3934/cpaa.2015.14.1357 |
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Mohamed Assellaou, Olivier Bokanowski, Hasnaa Zidani. Error estimates for second order Hamilton-Jacobi-Bellman equations. Approximation of probabilistic reachable sets. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 3933-3964. doi: 10.3934/dcds.2015.35.3933 |
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Shitao Liu, Roberto Triggiani. Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness. Conference Publications, 2011, 2011 (Special) : 1001-1014. doi: 10.3934/proc.2011.2011.1001 |
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Yufeng Shi, Qingfeng Zhu. A Kneser-type theorem for backward doubly stochastic differential equations. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1565-1579. doi: 10.3934/dcdsb.2010.14.1565 |
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Viorel Barbu. Existence for nonlinear finite dimensional stochastic differential equations of subgradient type. Mathematical Control and Related Fields, 2018, 8 (3&4) : 501-508. doi: 10.3934/mcrf.2018020 |
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Josef Diblík, Zdeněk Svoboda. Existence of strictly decreasing positive solutions of linear differential equations of neutral type. Discrete and Continuous Dynamical Systems - S, 2020, 13 (1) : 67-84. doi: 10.3934/dcdss.2020004 |
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Minghui Song, Liangjian Hu, Xuerong Mao, Liguo Zhang. Khasminskii-type theorems for stochastic functional differential equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1697-1714. doi: 10.3934/dcdsb.2013.18.1697 |
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Yongxin Jiang, Can Zhang, Zhaosheng Feng. A Perron-type theorem for nonautonomous differential equations with different growth rates. Discrete and Continuous Dynamical Systems - S, 2017, 10 (5) : 995-1008. doi: 10.3934/dcdss.2017052 |
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Xiaofei He, X. H. Tang. Lyapunov-type inequalities for even order differential equations. Communications on Pure and Applied Analysis, 2012, 11 (2) : 465-473. doi: 10.3934/cpaa.2012.11.465 |
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