Analysis of a model of the glucose-insulin regulatory system with two delays
Abstract
We continue a recent attempt to better understand the glucose‐insulin regulatory system via a mathematical model of delay differential equations with two discrete time delays. With explicit delays, the model is more realistic in physiology, more accurate in mathematics, and more robust in applications. We study this model analytically and perform carefully designed numerical simulations by allowing two parameters to vary. Our analytical and numerical results confirm most current existing physiological observations and reveal more insightful information. The following factors are critical for ensuring the sustained oscillatory regulation and insulin secretion: (1) the time lag for insulin secretion stimulated by glucose and the newly synthesized insulin becoming “remote insulin” (Theorem 4.2 (b) and Theorem 5.6); (2) the delayed effect of hepatic glucose production (Theorem 4.2 (c) and Theorem 5.6); (3) moderate insulin clearance rate (Theorem 5.6 and simulations in section 6.4); and (4) nonoverwhelming glucose infusion (simulations in section 6.2, 6.3, and 6.4).
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Time delays are common in modeling the metabolic system.
“Time delays, which are common in modeling the metabolic system (82–85), may induce uncertainty and make machine learning challenging to capture chaotic phenomena (86, 87).”
From The progression of secondary diabetes: A review of modeling studies (2022) · cites this paper as [84]
Cites
Delay differential equations with applications in population dynamics
(1993) · Mathematics and Computers in Simulation · doi:10.1016/0378-4754(93)90045-v · Cited by 3,240 · see citing works
Keener, J. P., & Sneyd, J. (2009) · Interdisciplinary applied mathematics · doi:10.1007/978-0-387-75847-3 · Cited by 2,213 · see citing works
Functions of One Complex Variable
Conway, J. B. (1973) · Graduate texts in mathematics · doi:10.1007/978-1-4615-9972-2 · Cited by 1,144 · see citing works
Insulin Degradation: Progress and Potential
Duckworth, W. C., Bennett, R. G., & Hamel, F. G. (1998) · Endocrine Reviews · doi:10.1210/edrv.19.5.0349 · Cited by 875 · see citing works
Knowler, W. C., Bennett, P. H., Hamman, R. F., & Miller, M. (1978) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a112648 · Cited by 601 · see citing works
Shampine, L. F., & Thompson, S. E. R. (2001) · Applied Numerical Mathematics · doi:10.1016/s0168-9274(00)00055-6 · Cited by 553 · see citing works
Makroglou, A., Li, J., & Kuang, Y. (2006) · Applied Numerical Mathematics · doi:10.1016/j.apnum.2005.04.023 · Cited by 367 · see citing works
Mathematical modelling of the intravenous glucose tolerance test
Gaetano, A. D., & Arino, O. (2000) · Journal of Mathematical Biology · doi:10.1007/s002850050007 · Cited by 353 · see citing works
Coefficients of normal blood glucose regulation
Bolie, V. W. (1961) · Journal of Applied Physiology · doi:10.1152/jappl.1961.16.5.783 · Cited by 349 · cited 4× · see citing works
“The exogenous glucose infusion rate can be larger when τ1 increases from [5, 15] for sustained regulatory oscillations to occur.”
BackgroundInfluentialInsulin Degradation: Progress and Potential
Duckworth, W. C. (1998) · Endocrine Reviews · doi:10.1210/er.19.5.608 · Cited by 344 · see citing works
A model of β-cell mass, insulin, and glucose kinetics: pathways to diabetes
TOPP, B., PROMISLOW, K., DEVRIES, G., MIURA, R. M., & FINEGOOD, D. T. (2000) · Journal of Theoretical Biology · doi:10.1006/jtbi.2000.2150 · Cited by 330 · see citing works
The evolution of β‐cell dysfunction and insulin resistance in type 2 diabetes
Bergman, R. N., Finegood, D. T., & Kahn, S. E. (2002) · European Journal of Clinical Investigation · doi:10.1046/j.1365-2362.32.s3.5.x · Cited by 302 · see citing works
Hirsch, W. M., Hanisch, H., & Gabriel, J.-P. (1985) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160380607 · Cited by 264 · see citing works
Computer model for mechanisms underlying ultradian oscillations of insulin and glucose
Sturis, J., Polonsky, K. S., Mosekilde, E., & Van Cauter, E. (1991) · American Journal of Physiology-Endocrinology and Metabolism · doi:10.1152/ajpendo.1991.260.5.e801 · Cited by 262 · cited 10× · see citing works
“These processes take a total of approximately 5–15 minutes [25], [26].”
BackgroundMethodResultInfluentialLi, J., Kuang, Y., & Mason, C. C. (2006) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2006.04.002 · Cited by 241 · see citing works
Pulsatile Insulin Secretion: Detection, Regulation, and Role in Diabetes
Pørksen, N., Hollingdal, M., Juhl, C., Butler, P., Veldhuis, J. D., & Schmitz, O. (2002) · Diabetes · doi:10.2337/diabetes.51.2007.s245 · Cited by 223 · see citing works
Modeling the Insulin–Glucose Feedback System: The Significance of Pulsatile Insulin Secretion
Tolić, I. M., Erik Mosekilde, B., & Sturis, J. (2000) · Journal of Theoretical Biology · doi:10.1006/jtbi.2000.2180 · Cited by 213 · see citing works
Prager, R., Wallace, P., & Olefsky, J. M. (1986) · Journal of Clinical Investigation · doi:10.1172/jci112599 · Cited by 204 · see citing works
The effect of physical exercise on the dynamics of glucose and insulin.
Derouich, M., & Boutayeb, A. (2002) · Journal of Biomechanics · doi:10.1016/s0021-9290(02)00055-6 · Cited by 184 · see citing works
Ultradian Oscillations of Insulin Secretion in Humans
Simon, C., & BRANDENBERGER, G. (2002) · Diabetes · doi:10.2337/diabetes.51.2007.s258 · Cited by 108 · see citing works
Analysis of IVGTT glucose-insulin interaction models with time delay
Li, J., Kuang, Y., & Li, B. (2001) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2001.1.103 · Cited by 94 · see citing works
Mukhopadhyay, A., Gaetano, A. D., & Arino, O. (2004) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2004.4.407 · Cited by 77 · see citing works
Bennett, D. L., & Gourley, S. A. (2003) · Applied Mathematics and Computation · doi:10.1016/s0096-3003(03)00332-1 · Cited by 68 · see citing works
Pathogenesis and prediction of diabetes mellitus: lessons from integrative physiology.
Bergman, R. N. (2002) · PubMed · Cited by 65 · see citing works
Physiological consequences of phasic insulin release in the normal animal
Cherrington, A. D., Sindelar, D., Edgerton, D., Steiner, K., & McGuinness, O. P. (2002) · Diabetes · doi:10.2337/diabetes.51.2007.s103 · Cited by 63 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Mathematical modeling of the glucose–insulin system: A review
Palumbo, P. J., Ditlevsen, S., BERTUZZI, A., & Gaetano, A. D. (2013) · Mathematical Biosciences · doi:10.1016/j.mbs.2013.05.006 · Cited by 183 · see citing works
Pawelek, K. A., Liu, S., Pahlevani, F., & Rong, L. (2011) · Mathematical Biosciences · doi:10.1016/j.mbs.2011.11.002 · Cited by 166 · see citing works
Modeling impulsive injections of insulin: towards artificial pancreas
Huang, M., Li, J., Song, X., & Guo, H. (2012) · SIAM Journal on Applied Mathematics · doi:10.1137/110860306 · Cited by 119 · see citing works
An, Q., Beretta, E., Kuang, Y., Wang, C., & Hao Wang, A. (2018) · Journal of Differential Equations · doi:10.1016/j.jde.2018.11.025 · Cited by 94 · see citing works
Mathematical modeling and qualitative analysis of insulin therapies
Wang, H., Li, J., & Kuang, Y. (2007) · Mathematical Biosciences · doi:10.1016/j.mbs.2007.05.008 · Cited by 65 · see citing works
Mathematical models of energy homeostasis
Pattaranit, R., & van den Berg, H. A. (2008) · Journal of The Royal Society Interface · doi:10.1098/rsif.2008.0216 · Cited by 61 · see citing works
Enhanced modelling of the glucose–insulin system and its applications in insulin therapies
Wang, H., Li, J., & Kuang, Y. (2008) · Journal of Biological Dynamics · doi:10.1080/17513750802101927 · Cited by 46 · see citing works
Analysis of HIV models with two time delays
Alshorman, A., Wang, X., Meyer, M. J., & Rong, L. (2016) · Journal of Biological Dynamics · doi:10.1080/17513758.2016.1148202 · Cited by 45 · see citing works
Ma, S.-H., Huo, H., & Meng, X.-Y. (2015) · Discrete Dynamics in Nature and Society · doi:10.1155/2015/260195 · Cited by 42 · see citing works
The range of time delay and the global stability of the equilibrium for an IVGTT model
Li, J., Wang, M., Gaetano, A. D., Palumbo, P. J., & Panunzi, S. (2011) · Mathematical Biosciences · doi:10.1016/j.mbs.2011.11.005 · Cited by 41 · see citing works
Complex dynamics of an epidemic model with saturated media coverage and recovery
Li, T., & Xiao, Y. (2022) · Nonlinear Dynamics · doi:10.1007/s11071-021-07096-6 · Cited by 40 · see citing works
Analysis of an Epidemic System with Two Response Delays in Media Impact Function
Song, P., & Xiao, Y. (2019) · Bulletin of Mathematical Biology · doi:10.1007/s11538-019-00586-0 · Cited by 40 · see citing works
Modeling impulsive insulin delivery in insulin pump with time delays
Song, X., Huang, M., & Li, J. (2014) · SIAM Journal on Applied Mathematics · doi:10.1137/130933137 · Cited by 35 · see citing works
Giang, D. V., Lenbury, Y., Gaetano, A. D., & Palumbo, P. J. (2008) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2008.02.016 · Cited by 30 · see citing works
Bernoulli wavelet method for non-linear fractional Glucose–Insulin regulatory dynamical system
Agrawal, K., Kumar, R., Kumar, S., Hadid, S. B., & Momani, S. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.112632 · Cited by 28 · see citing works
Physiological analysis on oscillatory behavior of glucose–insulin regulation by model with delays
Wu, Z., Chui, C., Hong, G. S., & Chang, S. K.-Y. (2011) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2011.03.032 · Cited by 28 · see citing works
Robust closed-loop control of plasma glycemia: A discrete-delay model approach
Palumbo, P. J., Pepe, P., Panunzi, S., & Gaetano, A. D. (2009) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2009.12.455 · Cited by 25 · see citing works
Saber, S., & Alalyani, A. (2022) · Mathematical Modelling and Analysis · doi:10.3846/mma.2022.14007 · Cited by 24 · see citing works
Reduction of interaction delays in networks
Lücken, L., Pade, J. P., Knauer, K. B., & Yanchuk, S. (2013) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/103/10006 · Cited by 23 · see citing works
Oscillatory dynamics of an intravenous glucose tolerance test model with delay interval
Shi, X., Kuang, Y., Makroglou, A., Mokshagundam, S. L., & Li, J. (2017) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5008384 · Cited by 23 · see citing works
Pei, L., Wang, Q., & Shi, H. (2010) · Nonlinear Dynamics · doi:10.1007/s11071-010-9812-5 · Cited by 22 · see citing works
Jaradat, M. A., Sawaqed, L., & Alzgool, M. (2020) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2020.101922 · Cited by 21 · see citing works
Mathematical modelling of glucose dynamics
Huard, B., & Kirkham, G. (2022) · Current Opinion in Endocrine and Metabolic Research · doi:10.1016/j.coemr.2022.100379 · Cited by 20 · see citing works
Robust closed-loop control of plasma glycemia: A discrete-delay model approach
Palumbo, P. J., Pepe, P., Panunzi, S., & Gaetano, A. D. (2008) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2008.4738940 · Cited by 20 · see citing works
A simple modeling framework for prediction in the human glucose–insulin system
Sirlanci, M., Levine, M. E., Wang, C. C. L., Albers, D. J., & Stuart, A. M. (2023) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0146808 · Cited by 19 · see citing works
Huard, B., Easton, J. F., & Angelova, M. N. (2015) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2015.02.017 · Cited by 19 · see citing works
Modelling the regulatory system for diabetes mellitus with a threshold window
Yang, J., Tang, S., & Cheke, R. (2014) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2014.08.012 · Cited by 17 · see citing works
Modeling and qualitative analysis of diabetes therapies with state feedback control
Huang, M., & Song, X. (2014) · International Journal of Biomathematics · doi:10.1142/s1793524514500351 · Cited by 17 · see citing works
Murillo, A. L., Li, J. X., & Castillo‐Chávez, C. (2019) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2019288 · Cited by 17 · see citing works
A Novel Model and its Analysis on the Metabolic Regulations of Glucose, Insulin, and Glucagon
Cohen, R. B., & Li, J. (2021) · SIAM Journal on Applied Mathematics · doi:10.1137/21m1390876 · Cited by 16 · see citing works
Yang, J., Tang, S., & Cheke, R. (2016) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2016.02.001 · Cited by 16 · see citing works
Huard, B., Bridgewater, A., & Angelova, M. N. (2017) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2017.01.039 · Cited by 17 · see citing works
Modeling Spruce Budworm Population Revisited: Impact of Physiological Structure on Outbreak Control
Vaidya, N. K., & Wu, J. (2008) · Bulletin of Mathematical Biology · doi:10.1007/s11538-007-9278-x · Cited by 16 · see citing works
Delay-induced uncertainty for a paradigmatic glucose–insulin model
Karamched, B., Hripcsak, G., Albers, D., & Ott, W. (2021) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0027682 · Cited by 12 · see citing works
McGrath, T., Murphy, K. G., & Jones, N. S. (2018) · Journal of The Royal Society Interface · doi:10.1098/rsif.2017.0736 · Cited by 10 · see citing works
Bifurcation analysis for the Kaldor–Kalecki model with two delays
Cao, J., & Hongyan, S. (2019) · Advances in Difference Equations · doi:10.1186/s13662-019-1948-0 · Cited by 10 · see citing works
Delay in ATP-dependent calcium inflow may affect insulin secretion from pancreatic beta-cell
Das, P. N., Halder, S., Bairagi, N., & Chatterjee, S. (2020) · Applied Mathematical Modelling · doi:10.1016/j.apm.2020.03.030 · Cited by 9 · see citing works
Strilka, R. J., Stull, M. C., Clemens, M. S., McCaver, S. C., & Armen, S. B. (2016) · Theoretical Biology and Medical Modelling · doi:10.1186/s12976-016-0029-2 · Cited by 9 · see citing works
Lücken, L., Pade, J. P., & Knauer, K. B. (2015) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/14097183x · Cited by 9 · see citing works
Analysis of a stochastic IVGTT glucose-insulin model with time delay
Shi, X., Zheng, Q., Yao, J., Li, J., & Zhou, X. (2020) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2020123 · Cited by 9 · see citing works
Rao, F., Zhang, Z., & Li, J. (2023) · Journal of Mathematical Biology · doi:10.1007/s00285-023-02003-6 · Cited by 8 · see citing works
Lawrence Aaron, P., Mendoza, R., & Mendoza, V. M. P. (2021) · AIP conference proceedings · doi:10.1063/5.0075363 · Cited by 8 · see citing works
Stable regions in the parameter space of delays for LTI fractional-order systems with two delays
Mesbahi, A., & Haeri, ء. (2014) · Signal Processing · doi:10.1016/j.sigpro.2014.03.012 · Cited by 8 · see citing works
Quantitative analysis of time delays of glucose - insulin dynamics using artificial pancreas
Rathee, S., & Nilam (2015) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2015.20.3115 · Cited by 8 · see citing works
Strilka, R. J., Armen, S. B., & INDECK, M. C. (2014) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2014.04.023 · Cited by 8 · see citing works
Karamched, B. R., Hripcsak, G., Leibel, R. L., Albers, D., & Ott, W. (2022) · Frontiers in Physiology · doi:10.3389/fphys.2022.936101 · Cited by 7 · see citing works
DDE Models of the Glucose-Insulin System: A Useful Tool for the Artificial Pancreas
Kong, J. D., Kumar, S. S., & Palumbo, P. J. (2014) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-319-03759-2_12 · Cited by 7 · see citing works
The progression of secondary diabetes: A review of modeling studies
Yang, B., Li, J., Haller, M. J., Schatz, D. A., & Rong, L. (2022) · Frontiers in Endocrinology · doi:10.3389/fendo.2022.1070979 · Cited by 6 · see citing works
A novel IVGTT model including interstitial insulin
Jin, J., Li, J., Xu, R., Yu, L., & Jin, Z. (2023) · Mathematics in Applied Sciences and Engineering · doi:10.5206/mase/15505 · Cited by 5 · see citing works
Modeling an artificial pancreas using retarded impulsive differential equation
Piper, L., Scolozzi, D., Lay-Ekuakille, A., Vergallo, P., Franchis, E. D., & Griffo, G. (2013) · IEEE International Symposium on Medical Measurements and Applications (MeMeA) · doi:10.1109/memea.2013.6549708 · Cited by 5 · see citing works
Global stability and periodicity in a glucose-insulin regulation model with a single delay
Angelova, M. N., Beliakov, G., Ivanov, A. F., & Shelyag, S. (2020) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2020.105659 · Cited by 5 · see citing works
A time-delay model of diabetic population: Dynamics analysis, sensitivity, and optimal control
Nasir, H. (2021) · Physica Scripta · doi:10.1088/1402-4896/ac1473 · Cited by 5 · see citing works
Effects of technological delay on insulin and blood glucose in a physiological model
Xu, J., & Pei, L. (2010) · International Journal of Non-Linear Mechanics · doi:10.1016/j.ijnonlinmec.2010.03.006 · Cited by 5 · see citing works
Stull, M. C., Strilka, R. J., Clemens, M. S., & Armen, S. B. (2015) · Journal of Diabetes Science and Technology · doi:10.1177/1932296815593291 · Cited by 5 · see citing works
Dynamics of a New Delayed Glucose–Insulin Model with Obesity
Gao, C., Chen, F., & Yu, P. (2024) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127424500706 · Cited by 4 · see citing works
Finite-time control of plasma glucose in insulin therapies for diabetes
Liu, S., Huang, M., Song, X., & Shi, X. (2018) · Advances in Difference Equations · doi:10.1186/s13662-018-1532-z · Cited by 4 · see citing works
Dai, L., Ou, S., Guo, Z., Wen, S., & Guan, Y. (2025) · Neurocomputing · doi:10.1016/j.neucom.2025.132008 · Cited by 3 · see citing works
Ultradian rhythms in glucose regulation: A mathematical assessment
Bridgewater, A., Stringer, B., Huard, B., & Angelova, M. N. (2019) · AIP conference proceedings · doi:10.1063/1.5095925 · Cited by 3 · see citing works
La inexistencia del ciclo de límite en un optimo problema de control de una población de diabéticos
Bernard, S., César, T., Nuiro, S. P., & Piétrus, A. (2018) · Revista de Matemática Teoría y Aplicaciones · doi:10.15517/rmta.v25i2.33692 · Cited by 3 · see citing works
Bifurcation analysis in a delay model of IVGTT glucose–insulin interaction
Mohabati, F., & Molaei, M. R. (2019) · Theory in Biosciences · doi:10.1007/s12064-019-00298-y · Cited by 3 · see citing works
Bridgewater, A., Huard, B., & Angelova, M. N. (2020) · Journal of Nonlinear Science · doi:10.1007/s00332-020-09612-1 · Cited by 3 · see citing works
Chishti, F., Hanif, F., & Shams, R. (2023) · Mathematical Sciences and Applications · doi:10.52700/msa.v2i1.6 · Cited by 2 · see citing works
Mathematical Modelling for Glucose Homeostasis and Associated Mechanisms: A State-of-the-Art Review
Lamlili, M. E. N., Boutayeb, W., & Boutayeb, A. (2025) · Industrial and applied mathematics · doi:10.1007/978-981-96-1925-2_2 · Cited by 2 · see citing works
Characteristic roots for two-lag linear delay differential equations
Bortz, D. M. (2016) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2016053 · Cited by 2 · see citing works
Optimal selection of injection doses and injection timings for insulin therapy in a limited time
Liu, S., Yu, L., Huang, M., & Shi, X. (2020) · Advances in Difference Equations · doi:10.1186/s13662-020-03111-z · Cited by 2 · see citing works
Modeling Impulsive Intake of Glucose: The Significance of Diet to Glucose-Insulin System
Shi, X., Yao, J., & Zhou, X. (2020) · Complexity · doi:10.1155/2020/6043629 · Cited by 1 · see citing works
Hopf Bifurcation Analysis of a Zika Virus Transmission Model with Two Time Delays
Meyvacı, M. (2025) · Journal of Mathematical Sciences and Modelling · doi:10.33187/jmsm.1607113 · Cited by 1 · see citing works
Dynamic analysis of an infectious disease model with media coverage and saturated treatment
Ma, C., Zhao, Y., & Tan, X. (2026) · Advances in Continuous and Discrete Models · doi:10.1186/s13662-026-04073-4 · Cited by 1 · see citing works
Stability of linear delay differential systems via Laplace transformation
Naeem, M., Kuang, Y., & Li, J. (2026) · Mathematical Biosciences · doi:10.1016/j.mbs.2026.109778 · Cited by 1 · see citing works
Dynamic analysis of a Filippov blood glucose insulin model
Wu, Q., Yu, L., Li, X.-Z., & Li, W. (2024) · AIMS Mathematics · doi:10.3934/math.2024895 · Cited by 1 · see citing works
Dynamics analysis in a delayed glucose-insulin model incorporating obesity
Gao, C., Chen, F., & Yu, P. (2024) · International Journal of Biomathematics · doi:10.1142/s1793524524501146 · Cited by 1 · see citing works
Strilka, R. J., Trexler, S. T., Sjulin, T. J., & Armen, S. B. (2017) · Informatics in Medicine Unlocked · doi:10.1016/j.imu.2017.12.002 · Cited by 1 · see citing works
Rapti, Z. (2020) · Nonlinear systems and complexity · doi:10.1007/978-3-030-44992-6_1 · Cited by 1 · see citing works
Synchrony and bifurcations in coupled dynamical systems and effects of time delay
Pade, J. P. (2015) · edoc Publication server (Humboldt University of Berlin) · doi:10.18452/17293 · Cited by 1 · see citing works
Mathematical models of health focusing on diabetes: Delay differential equations and data mining
Easton, J. F. (2015) · Northumbria Research Link (Northumbria University)
The Approach to Model Building
Laugesen, J. L., & Erik Mosekilde, B. (2011) · Springer eBooks · doi:10.1007/978-3-7091-0418-7_3
Type 2 Diabetes and Obesity: A Biological, Behavioral, and Environmental Context
Murillo, A. L. (2016)
Sathe, A. M. (2018) · Journal of Bioengineering and Biomedical Sciences · doi:10.4172/2155-9538.1000256
Trigonometric-Type Functions Derived from Polygons Inscribed in the Unit Circle
Lewis, T. (2019) · Association for Women in Mathematics series · doi:10.1007/978-3-030-19486-4_19
A dynamical model and bifurcation analysis for glucagon and glucose regulatory system
Mohabati, F., Molaei, M. R., & Waezizadeh, T. (2019) · Journal of Information and Optimization Sciences · doi:10.1080/02522667.2019.1630937
Dynamics of a stochastic glucose-insulin model with impulsive injection of insulin
(2020) · Communications in Mathematical Biology and Neuroscience · doi:10.28919/cmbn/4390
Hussain, R., Arbab, A., Salahuddin, S., Munir, M., Kausar, N., & Ali, A. (2020) · International Journal of Analysis and Applications · doi:10.28924/2291-8639-18-2020-939
МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВІЛ ІЗ ЗАТРИМКОЮ
Зеленський, К., & Самоловов, Є. (2019) · Modern engineering and innovative technologies · doi:10.30890/2567-5273.2022-24-02-014
Multistability Switches and Codimension-2 Bifurcation in an SIRS(Z) Model with Two Delays
Das, T., Srivastava, P. K., & Singh, S. (2023) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127423501250
Implementation strategy of insulin therapy under sparse state feedback
Huang, M., & Liu, S. (2024) · Applied Mathematics Letters · doi:10.1016/j.aml.2024.109347
Laplace Transform in Stability Analysis of Differential Systems with Delay Interval
Verriest, E. I., & Kuang, Y. (2025) · MATRIX book series · doi:10.1007/978-3-031-76738-8_27
Ruschel, S., & Huard, B. (2025) · The ANZIAM Journal · doi:10.1017/s1446181125100084
Adaptive Parallel Methods for Polynomial Equations with Unknown Multiplicity
Shams, M., & Carpentieri, B. (2025) · Algorithms · doi:10.3390/a19010021
Yasmeen, F., Akhter, M. M., & Maheshwari, R. (2026) · Communications in computer and information science · doi:10.1007/978-3-032-09572-5_3
Qualitative analysis of a glucose-insulin dynamics model with time delay in insulin action
Liu, S., Li, J., Ma, L., & Zhang, K. (2026) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2026063
Dynamics of a multi-delay glucose-insulin-glucagon system under dual-hormone impulsive control
Liu, S., Lu, T., & Huang, M. (2026) · Advances in Continuous and Discrete Models · doi:10.1186/s13662-026-04094-z
Dalton, M., Asante-Asamani, E. O., & Greene, J. M. (2026) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2026060
Integrator Sensitivity of Chaos in the Ultradian Glucose-Insulin Model
Sinha, A., Chowdhury, S., & Roychowdhury, S. (2026) · EPJ Web of Conferences · doi:10.1051/epjconf/202637001012
Dynamical analysis and bifurcation study of an epidemic model with media coverage and time delay
Ma, C., Zhao, Y., Tan, X., & Shi, W. (2026) · Networks and Heterogeneous Media · doi:10.3934/nhm.2026061
A stage structured predator–prey system with time delays and fear effect
Li, L., Liu, J., & Zhang, T. (2026) · Electronic journal of qualitative theory of differential equations · doi:10.14232/ejqtde.2026.1.29
- Authors
- Li, J., & Kuang, Y.
- Affiliations
- University of Louisville (US)
- ORCID
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 2007-01
- Volume
- 67
- Issue
- 3
- Pages
- 757-776
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W2123658935
- Cited by
- 96
- References
- 25
- Citations by year
- 2026: 9 · 2025: 6 · 2024: 4 · 2023: 5 · 2022: 6 · 2021: 4 · 2020: 10 · 2019: 8 · 2018: 6 · 2017: 3 · 2016: 5 · 2015: 7 · 2014: 6 · 2013: 3 · 2012: 1
- FWCI
- 2.99
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- SIAM Journal on Applied Mathematics (publishedVersion)
- Topics
- Health Sciences › Medicine › Surgery › Pancreatic function and diabetes
- Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Differential Equations Analysis
- Keywords
- glucose-insulin regulatory system, delay differential equations, insulin secretion, hepatic glucose production, glucose infusion
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
