Food choices and body weight changes: A mathematical model analysis

Mantana Chudtong; Andrea De Gaetano; Mantana Chudtong; Andrea De Gaetano

doi:10.3934/mbe.2025065

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 7: 1790-1824. doi: 10.3934/mbe.2025065

Previous Article Next Article

Research article

Food choices and body weight changes: A mathematical model analysis

Mantana Chudtong ^{1,2
,
,},
Andrea De Gaetano ^1,3,4

1.
Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
2.
Center of Excellence in Mathematics, the Commission on Higher Education, Si Ayutthaya Rd., Bangkok 10400, Thailand
3.
National Research Council of Italy (IRIB-CNR and IASI-CNR), Palermo and Rome, Italy
4.
Dept. of Biomatics, Óbuda University, Budapest, Hungary

Received: 10 January 2025 Revised: 15 March 2025 Accepted: 19 May 2025 Published: 05 June 2025

A short–term stochastic model of minute–by–minute food intake is formulated, incorporating the interaction of appetite, insulinemia, and glycemia in determining the size and frequency of meals. By assuming a person would maintain his or her eating habit over time, we extend the simulation period to several years and explore scenarios based on food choices (high–fiber vs. high–carbohydrate) or appetite suppression. The model coherently predicts increments or decrements in body weight in the long–term when altering appetite in the short–term. Further, the model shows how food type choice, at the same appetite drive and habitual proposed meal size, induces macroscopic changes in body weight over a very few years. The model is innovative in that it connects the minute–by–minute behavior of the individual with long–term changes in metabolic compensation, in insulin sensitivity, in glycemic variability, and eventually in body size, thus helping to interpret the long–term development of Type 2 diabetes mellitus resulting from an unhealthy lifestyle.
- body weight,
- mathematical modeling,
- glycemia,
- insulin resistance,
- obesity,
- energy expenditure,
- metabolism,
- ordinary differential equations,
- food intake
Citation: Mantana Chudtong, Andrea De Gaetano. Food choices and body weight changes: A mathematical model analysis[J]. Mathematical Biosciences and Engineering, 2025, 22(7): 1790-1824. doi: 10.3934/mbe.2025065

Related Papers:

Abstract

A short–term stochastic model of minute–by–minute food intake is formulated, incorporating the interaction of appetite, insulinemia, and glycemia in determining the size and frequency of meals. By assuming a person would maintain his or her eating habit over time, we extend the simulation period to several years and explore scenarios based on food choices (high–fiber vs. high–carbohydrate) or appetite suppression. The model coherently predicts increments or decrements in body weight in the long–term when altering appetite in the short–term. Further, the model shows how food type choice, at the same appetite drive and habitual proposed meal size, induces macroscopic changes in body weight over a very few years. The model is innovative in that it connects the minute–by–minute behavior of the individual with long–term changes in metabolic compensation, in insulin sensitivity, in glycemic variability, and eventually in body size, thus helping to interpret the long–term development of Type 2 diabetes mellitus resulting from an unhealthy lifestyle.

References

[1]	Obesity and overweight, URL https://www.who.int/news-room/fact-sheets/detail/obesity-and-overweight.
[2]	N. J. Temple, The origins of the obesity epidemic in the USA–lessons for today, Nutrients, 14 (2022), 4253. https://doi.org/10.3390/nu14204253 doi: 10.3390/nu14204253
[3]	S. Bleich, D. Cutler, C. Murray, A. Adams, Why is the developed world obese?, Annu. Rev. Public Health, 29 (2008), 273–295. https://doi.org/10.1146/annurev.publhealth.29.020907.090954 doi: 10.1146/annurev.publhealth.29.020907.090954
[4]	M. Ng, T. Fleming, M. Robinson, B. Thomson, N. Graetz, C. Margono, et al., Global, regional, and national prevalence of overweight and obesity in children and adults during 1980-2013: A systematic analysis for the global burden of disease study 2013, Lancet (London, England), 384 (2014), 766–781. https://doi.org/10.1016/S0140-6736(14)60460-8 doi: 10.1016/S0140-6736(14)60460-8
[5]	H. F. Wells, J. C. Buzby, Dietary assessment of major trends in U.S. food consumption, 1970–2005. URL http://www.ers.usda.gov/publications/pub-details/?pubid = 44220.
[6]	Y. Ritze, G. Bárdos, J. G. D'Haese, B. Ernst, M. Thurnheer, B. Schultes, S. C. Bischoff, Effect of high sugar intake on glucose transporter and weight regulating hormones in mice and humans, PLOS ONE, 9 (2014), e101702. https://doi.org/10.1371/journal.pone.0101702 doi: 10.1371/journal.pone.0101702
[7]	L. T. Morenga, S. Mallard, J. Mann, Dietary sugars and body weight: Systematic review and meta-analyses of randomised controlled trials and cohort studies, BMJ, 346 (2013), e7492. https://doi.org/10.1136/bmj.e7492 doi: 10.1136/bmj.e7492
[8]	H. Gu, S. Shao, J. Liu, Z. Fan, Y. Chen, J. Ni, et al., Age- and sex-associated impacts of body mass index on stroke type risk: a 27-year prospective cohort study in a low-income population in China, Front. Neurol., 10 (2019). https://doi.org/10.3389/fneur.2019.00456 doi: 10.3389/fneur.2019.00456
[9]	K. Cheng, Health oriented lifelong nutrition controls: Preventing cardiovascular diseases caused by obesity, 2020, URL /paper/Health-Oriented-Lifelong-Nutrition-Controls%3A-Caused-Cheng/e8ba816f29502370121f6c44217d019fcbae0223.
[10]	K. Mc Namara, H. Alzubaidi, J. K. Jackson, Cardiovascular disease as a leading cause of death: how are pharmacists getting involved?, Integr. Pharm. Res. Pract., 8 (2019), 1–11. https://doi.org/10.2147/IPRP.S133088 doi: 10.2147/IPRP.S133088
[11]	N. Taghizadeh, H. M. Boezen, J. P. Schouten, C. P. Schröder, E. G. E. de Vries, J. M. Vonk, BMI and lifetime changes in BMI and cancer mortality risk, PLoS ONE, 10. https://doi.org/10.1371/journal.pone.0125261
[12]	K. Bhaskaran, I. Douglas, H. Forbes, I. dos Santos-Silva, D. A. Leon, L. Smeeth, Body-mass index and risk of 22 specific cancers: A population-based cohort study of 5·24 million UK adults, The Lancet, 384 (2014), 755–765. https://doi.org/10.1016/S0140-6736(14)60892-8 doi: 10.1016/S0140-6736(14)60892-8
[13]	M. Kalligeros, F. Shehadeh, E. K. Mylona, G. Benitez, C. G. Beckwith, P. A. Chan, et al., Association of obesity with disease severity among patients with coronavirus disease 2019, Obesity, 28 (2020), 1200–1204. https://doi.org/10.1002/oby.22859 doi: 10.1002/oby.22859
[14]	A. Golay, J. Ybarra, Link between obesity and type 2 diabetes, Best Pract Res. Clin. Endocrinol Metab., 19 (2005), 649–663. https://doi.org/10.1016/j.beem.2005.07.010 doi: 10.1016/j.beem.2005.07.010
[15]	A. S. Al-Goblan, M. A. Al-Alfi, M. Z. Khan, Mechanism linking diabetes mellitus and obesity, Diabetes Metab. Syndr. Obes., 7 (2014), 587–591. https://doi.org/10.2147/DMSO.S67400 doi: 10.2147/DMSO.S67400
[16]	A. S. Barnes, The epidemic of obesity and diabetes, Tex. Heart Inst. J., 38 (2011), 142–144. URL https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3066828/.
[17]	N. A. Roper, R. W. Bilous, W. F. Kelly, N. C. Unwin, V. M. Connolly, Cause-specific mortality in a population with diabetes: south tees diabetes mortality study, Diabetes Care, 25 (2002), 43–48. https://doi.org/10.2337/diacare.25.1.43 doi: 10.2337/diacare.25.1.43
[18]	M. Tancredi, A. Rosengren, A.-M. Svensson, M. Kosiborod, A. Pivodic, S. Gudbjörnsdottir, et al., Excess mortality among persons with type 2 diabetes, NEJM, 373 (2015), 1720–1732. https://doi.org/10.1056/NEJMoa1504347 doi: 10.1056/NEJMoa1504347
[19]	R. A. DeFronzo, R. C. Bonadonna, E. Ferrannini, Pathogenesis of NIDDM: a balanced overview, Diabetes Care, 15 (1992), 318–368. https://doi.org/10.2337/diacare.15.3.318 doi: 10.2337/diacare.15.3.318
[20]	A. D. Baron, G. Brechtel, P. Wallace, S. V. Edelman, Rates and tissue sites of non-insulin- and insulin-mediated glucose uptake in humans, Am. J. Physiol. Endocrinol Metab., 255 (1988), E769–E774. https://doi.org/10.1152/ajpendo.1988.255.6.E769 doi: 10.1152/ajpendo.1988.255.6.E769
[21]	R. A. DeFronzo, D. Tripathy, Skeletal muscle insulin resistance is the primary defect in type 2 diabetes, Diabetes Care, 32 (2009), S157–S163. https://doi.org/10.2337/dc09-S302 doi: 10.2337/dc09-S302
[22]	R. A. DeFronzo, The triumvirate: -cell, muscle, liver: A collusion responsible for NIDDM, Diabetes, 37 (1988), 667–687. https://doi.org/10.2337/diab.37.6.667 doi: 10.2337/diab.37.6.667
[23]	E. Archer, C. J. Lavie, J. O. Hill, The contributions of 'diet', 'genes', and physical activity to the etiology of obesity: contrary evidence and consilience, Prog. Cardiovasc. Dis., 61 (2018), 89–102. https://doi.org/10.1016/j.pcad.2018.06.002 doi: 10.1016/j.pcad.2018.06.002
[24]	E. Archer, G. Pavela, S. McDonald, C. J. Lavie, J. O. Hill, Cell-specific "competition for calories" drives asymmetric nutrient-energy partitioning, obesity, and metabolic diseases in human and non-human Animals, Front. Physiol., 9 (2018), 1053. https://doi.org/10.3389/fphys.2018.01053 doi: 10.3389/fphys.2018.01053
[25]	A. V. Greco, G. Mingrone, A. Giancaterini, M. Manco, M. Morroni, S. Cinti, et al., Insulin resistance in morbid obesity: reversal with intramyocellular fat depletion, Diabetes, 51 (2002), 144–151. https://doi.org/10.2337/diabetes.51.1.144 doi: 10.2337/diabetes.51.1.144
[26]	O. T. Hardy, M. P. Czech, S. Corvera, What causes the insulin resistance underlying obesity?, Curr. Opin. Endocrinol. Diabetes Obes., 19 (2012), 81–87. https://doi.org/10.1097/MED.0b013e3283514e13 doi: 10.1097/MED.0b013e3283514e13
[27]	C. Roberts-Toler, B. T. O'Neill, A. M. Cypess, Diet-induced obesity causes insulin resistance in mouse brown adipose tissue: DIO causes BAT insulin resistance, Obesity, 23 (2015), 1765–1770. https://doi.org/10.1002/oby.21134 doi: 10.1002/oby.21134
[28]	E. Christiansen, L. Garby, Prediction of body weight changes caused by changes in energy balance, Eur. J. Clin. Invest., 32 (2002), 826–830. https://doi.org/10.1046/j.1365-2362.2002.01036.x doi: 10.1046/j.1365-2362.2002.01036.x
[29]	E. Christiansen, L. Garby, T. I. A. Sørensen, Quantitative analysis of the energy requirements for development of obesity, J. Theor. Biol., 234 (2005), 99–106. https://doi.org/10.1016/j.jtbi.2004.11.012 doi: 10.1016/j.jtbi.2004.11.012
[30]	C. C. Chow, K. D. Hall, The dynamics of human body weight change, PLoS Comput. Biol., 4 (2008), e1000045. https://doi.org/10.1371/journal.pcbi.1000045 doi: 10.1371/journal.pcbi.1000045
[31]	K. D. Hall, P. N. Jordan, Modeling weight-loss maintenance to help prevent body weight regain, Am. J. Clin. Nutr., 88 (2008), 1495–1503. https://doi.org/10.3945/ajcn.2008.26333 doi: 10.3945/ajcn.2008.26333
[32]	D. M. Thomas, A. Ciesla, J. A. Levine, J. G. Stevens, C. K. Martin, A mathematical model of weight change with adaptation, MBE, 6 (2009), 873–887. https://doi.org/10.3934/mbe.2009.6.873 doi: 10.3934/mbe.2009.6.873
[33]	E. H. Livingston, I. Kohlstadt, Simplified resting metabolic rate-predicting formulas for normal-sized and obese individuals, Obes. Res., 13 (2005), 1255–1262. https://doi.org/10.1038/oby.2005.149 doi: 10.1038/oby.2005.149
[34]	D. M. Thomas, C. K. Martin, S. Heymsfield, L. M. Redman, D. A. Schoeller, J. A. Levine, A simple model predicting individual weight change in humans, J. Biol. Dyn., 5 (2011), 579–599. https://doi.org/10.1080/17513758.2010.508541 doi: 10.1080/17513758.2010.508541
[35]	J. Guo, D. C. Brager, K. D. Hall, Simulating long-term human weight-loss dynamics in response to calorie restriction, Am. J. Clin. Nutr., 107 (2018), 558–565. https://doi.org/10.1093/ajcn/nqx080 doi: 10.1093/ajcn/nqx080
[36]	P. Jacquet, Y. Schutz, J.-P. Montani, A. Dulloo, How dieting might make some fatter: modeling weight cycling toward obesity from a perspective of body composition autoregulation, Int. J. Obes., 44 (2020), 1243–1253. https://doi.org/10.1038/s41366-020-0547-1 doi: 10.1038/s41366-020-0547-1
[37]	A. Peña Fernández, A. Youssef, C. Heeren, C. Matthys, J.-M. Aerts, Real-time model predictive control of human bodyweight based on energy intake, Appl. Sci., 9 (2019), 2609. https://doi.org/10.3390/app9132609 doi: 10.3390/app9132609
[38]	O. Babajide, T. Hissam, P. Anna, G. Anatoliy, A. Astrup, J. Alfredo Martinez, et al., A machine learning approach to short-term body weight prediction in a dietary intervention program, Computational Science – ICCS 2020. Lecture Notes in Computer Science, Springer International Publishing, Cham, 2020,441–455.
[39]	K. D. Hall, G. Sacks, D. Chandramohan, C. C. Chow, Y. C. Wang, S. L. Gortmaker, et al., Quantification of the effect of energy imbalance on bodyweight, Lancet (London, England), 378 (2011), 826–837. https://doi.org/10.1016/S0140-6736(11)60812-X doi: 10.1016/S0140-6736(11)60812-X
[40]	B.-H. Lin, T. A. Smith, J.-Y. Lee, K. D. Hall, Measuring weight outcomes for obesity intervention strategies: the case of a sugar-sweetened beverage tax, Econ. Hum. Biol., 9 (2011), 329–341. https://doi.org/10.1016/j.ehb.2011.08.007 doi: 10.1016/j.ehb.2011.08.007
[41]	T. A. Smith, Taxing Caloric Sweetened Beverages: Potential Effects on Beverage Consumption, Calorie Intake, and Obesity, DIANE Publishing, 2010, Google-Books-ID: 3hBCqYKh0JQC.
[42]	T. S. Church, D. M. Thomas, C. Tudor-Locke, P. T. Katzmarzyk, C. P. Earnest, R. Q. Rodarte, et al., Trends over 5 decades in U.S. occupation-related physical activity and their associations with obesity, PLOS ONE, 6 (2011), e19657. https://doi.org/10.1371/journal.pone.0019657 doi: 10.1371/journal.pone.0019657
[43]	K. D. Hall, Metabolism of mice and men: mathematical modeling of body weight dynamics, Curr. Opin. Clin. Nutr. Metab. Care, 15 (2012), 418–423. https://doi.org/10.1097/MCO.0b013e3283561150 doi: 10.1097/MCO.0b013e3283561150
[44]	K. D. Hall, J. Guo, M. Dore, C. C. Chow, The progressive increase of food waste in America and its environmental impact, PLOS ONE, 4 (2009), e7940. https://doi.org/10.1371/journal.pone.0007940 doi: 10.1371/journal.pone.0007940
[45]	F. P. Kozusko, Body weight setpoint, metabolic adaption and human starvation, Bull. Math. Biol., 63 (2001), 393–403. https://doi.org/10.1006/bulm.2001.0229 doi: 10.1006/bulm.2001.0229
[46]	F. P. Kozusko, The effects of body composition on setpoint based weight loss, Math. Comput. Model., 35 (2002), 973–982. https://doi.org/10.1016/S0895-7177(02)00064-X doi: 10.1016/S0895-7177(02)00064-X
[47]	D. M. Thomas, J. E. Navarro-Barrientos, D. E. Rivera, S. B. Heymsfield, C. Bredlau, L. M. Redman, et al., Dynamic energy-balance model predicting gestational weight gain, Am. J. Clin. Nutr., 95 (2012), 115–122. https://doi.org/10.3945/ajcn.111.024307 doi: 10.3945/ajcn.111.024307
[48]	K. Ejima, D. M. Thomas, D. B. Allison, A mathematical model for predicting obesity transmission with both genetic and nongenetic heredity, Obesity (Silver Spring), 26 (2018), 927–933. https://doi.org/10.1002/oby.22135 doi: 10.1002/oby.22135
[49]	K. D. Hall, Computational model of in vivo human energy metabolism during semistarvation and refeeding, Am. J. Physiol. Endocrinol. Metab., 291 (2006), E23–37. https://doi.org/10.1152/ajpendo.00523.2005 doi: 10.1152/ajpendo.00523.2005
[50]	D.-M. Li, T.-N. Guo, Q. Wang, B. Chai, R.-X. Zhang, D.-M. Li, et al., Quantitative analysis of body metabolism regulation model in the process of weight loss, AIMS Math., 5 (2020), 2500–2525. https://doi.org/10.3934/math.2020165 doi: 10.3934/math.2020165
[51]	G. M. Barnwell, F. S. Stafford, Mathematical model for decision-making neural circuits controlling food intake, Bull. Psychon. Soc., 5 (1975), 473–476. https://doi.org/10.3758/BF03333304 doi: 10.3758/BF03333304
[52]	R. C. Boston, P. J. Moate, K. C. Allison, J. D. Lundgren, A. J. Stunkard, Modeling circadian rhythms of food intake by means of parametric deconvolution: results from studies of the night eating syndrome, Am. J. Clin. Nutr., 87 (2008), 1672–1677. https://doi.org/10.1093/ajcn/87.6.1672 doi: 10.1093/ajcn/87.6.1672
[53]	F. Cameron, G. Niemeyer, B. A. Buckingham, Probabilistic evolving meal detection and estimation of meal total glucose appearance, J. Diabetes Sci. Technol., 3 (2009), 1022–1030. https://doi.org/10.1177/193229680900300505 doi: 10.1177/193229680900300505
[54]	N. P. Balakrishnan, L. Samavedham, G. P. Rangaiah, Personalized mechanistic models for exercise, meal and insulin interventions in children and adolescents with type 1 diabetes, J. Theor. Biol., 357 (2014), 62–73. https://doi.org/10.1016/j.jtbi.2014.04.038 doi: 10.1016/j.jtbi.2014.04.038
[55]	M. Jacquier, F. Crauste, C. O. Soulage, H. A. Soula, A predictive model of the dynamics of body weight and food intake in rats submitted to caloric restrictions, PLOS ONE, 9 (2014), e100073. https://doi.org/10.1371/journal.pone.0100073 doi: 10.1371/journal.pone.0100073
[56]	A. L. Murillo, M. Safan, C. Castillo-Chavez, E. D. C. Phillips, D. Wadhera, Modeling eating behaviors: The role of environment and positive food association learning via a ratatouille effect, MBE, 13, 841–855. https://doi.org/10.3934/mbe.2016020
[57]	M. Chudtong, A. D. Gaetano, A mathematical model of food intake, MBE, 18 (2021), 1238–1279. https://doi.org/10.3934/mbe.2021067 doi: 10.3934/mbe.2021067
[58]	A. Hinsberger, B. K. Sandhu, Digestion and absorption, Curr. Pediatr., 14 (2004), 605–611. https://doi.org/10.1016/j.cupe.2004.08.004 doi: 10.1016/j.cupe.2004.08.004
[59]	A. D. Jackson, J. McLaughlin, Digestion and absorption, Surgery (Oxf), 27 (2009), 231–236. https://doi.org/10.1016/j.mpsur.2009.03.003 doi: 10.1016/j.mpsur.2009.03.003
[60]	I. Campbell, Digestion and absorption, Anaesth. Intensive Care Med., 13 (2012), 62–63. https://doi.org/10.1016/j.mpaic.2011.11.001 doi: 10.1016/j.mpaic.2011.11.001
[61]	P. R. Kiela, F. K. Ghishan, Physiology of intestinal absorption and secretion, Best Pract. Res. Clin. Gastroenterol., 30 (2016), 145–159. https://doi.org/10.1016/j.bpg.2016.02.007 doi: 10.1016/j.bpg.2016.02.007
[62]	A. B. Strathe, A. Danfær, A. Chwalibog, A dynamic model of digestion and absorption in pigs, Anim. Feed Sci. Technol., 143 (2008), 328–371. https://doi.org/10.1016/j.anifeedsci.2007.05.018 doi: 10.1016/j.anifeedsci.2007.05.018
[63]	S. Salinari, A. Bertuzzi, G. Mingrone, Intestinal transit of a glucose bolus and incretin kinetics: a mathematical model with application to the oral glucose tolerance test, Am. J. Physiol. Endocrinol. Metab., 300 (2011), E955–965. https://doi.org/10.1152/ajpendo.00451.2010 doi: 10.1152/ajpendo.00451.2010
[64]	A. D. Gaetano, S. Panunzi, A. Matone, A. Samson, J. Vrbikova, B. Bendlova, et al., Routine OGTT: a robust model including incretin effect for precise identification of insulin sensitivity and secretion in a single individual, PLOS ONE, 8 (2013), e70875. https://doi.org/10.1371/journal.pone.0070875 doi: 10.1371/journal.pone.0070875
[65]	M. Taghipoor, G. Barles, C. Georgelin, J. R. Licois, P. Lescoat, Digestion modeling in the small intestine: impact of dietary fiber, Math. Biosci., 258 (2014), 101–112. https://doi.org/10.1016/j.mbs.2014.09.011 doi: 10.1016/j.mbs.2014.09.011
[66]	E. D. Lehmann, T. Deutsch, A physiological model of glucose-insulin interaction in type 1 diabetes mellitus, J. Biomed. Eng., 14 (1992), 235–242. https://doi.org/10.1016/0141-5425(92)90058-s doi: 10.1016/0141-5425(92)90058-s
[67]	A. Roy, R. S. Parker, Dynamic modeling of exercise effects on plasma glucose and insulin levels, J. Diabetes Sci. Technol., 1 (2007), 338–347. https://doi.org/10.1177/193229680700100305 doi: 10.1177/193229680700100305
[68]	R. Hovorka, V. Canonico, L. J. Chassin, U. Haueter, M. Massi-Benedetti, M. Orsini Federici, et al., Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes, Physiol. Meas., 25 (2004), 905–920. https://doi.org/10.1088/0967-3334/25/4/010 doi: 10.1088/0967-3334/25/4/010
[69]	B. K. Mani, K. Shankar, J. M. Zigman, Ghrelin's relationship to blood glucose, Endocrinol., 160 (2019), 1247–1261. https://doi.org/10.1210/en.2019-00074 doi: 10.1210/en.2019-00074
[70]	R. D. Palmiter, Is dopamine a physiologically relevant mediator of feeding behavior?, Trends Neurosci., 30 (2007), 375–381. https://doi.org/10.1016/j.tins.2007.06.004 doi: 10.1016/j.tins.2007.06.004
[71]	D. P. Figlewicz, S. B. Evans, J. Murphy, M. Hoen, D. G. Baskin, Expression of receptors for insulin and leptin in the ventral tegmental area/substantia nigra (VTA/SN) of the rat, Brain Res., 964 (2003), 107–115. https://doi.org/10.1016/S0006-8993(02)04087-8 doi: 10.1016/S0006-8993(02)04087-8
[72]	D. P. Figlewicz, P. Szot, M. Chavez, S. C. Woods, R. C. Veith, Intraventricular insulin increases dopamine transporter mRNA in rat VTA/substantia nigra, Brain Res., 644 (1994), 331–334. https://doi.org/10.1016/0006-8993(94)91698-5 doi: 10.1016/0006-8993(94)91698-5
[73]	J. Vartiainen, Ghrelin, obesity and type 2 diabetes : Genetic, metabolic and epidemiological studies, University of Oulu, Place: University of Oulu.
[74]	J. L. Jameson, L. J. D. Groot, Endocrinology: Adult and Pediatric, E-Book, Elsevier Health Sciences, 2015, Google-Books-ID: xmLeBgAAQBAJ.
[75]	D. A. Schatz, M. Haller, M. Atkinson, Type 1 Diabetes, An Issue of Endocrinology and Metabolism Clinics of North America, E-Book, Elsevier Health Sciences, 2010, Google-Books-ID: nu2IxmYJkjkC.
[76]	J. Morales, D. Schneider, Hypoglycemia, AJM, 127 (2014), S17–S24. https://doi.org/10.1016/j.amjmed.2014.07.004 doi: 10.1016/j.amjmed.2014.07.004
[77]	C. Kenny, When hypoglycemia is not obvious: Diagnosing and treating under-recognized and undisclosed hypoglycemia, Prim. Care Diabetes, 8 (2014), 3–11. https://doi.org/10.1016/j.pcd.2013.09.002 doi: 10.1016/j.pcd.2013.09.002
[78]	G. Cheney, Medical Management of Gastrointestinal Disorders, Year Book, 1950, Google-Books-ID: nwiyAAAAIAAJ.
[79]	M. M, How to Manage Your Diabetes and Lead a Normal Life, Peacock Books, 2008, Google-Books-ID: bavxjgZa2NIC.
[80]	R. K. Bernstein, Hunger–a common symptom of hypoglycemia, Diabetes Care, 16 (1993), 1049. https://doi.org/10.2337/diacare.16.7.1049a doi: 10.2337/diacare.16.7.1049a
[81]	L. C. Perlmuter, B. P. Flanagan, P. H. Shah, S. P. Singh, Glycemic control and hypoglycemia, Diabetes Care, 31 (2008), 2072–2076. https://doi.org/10.2337/dc08-1441 doi: 10.2337/dc08-1441
[82]	B. Schultes, K. M. Oltmanns, W. Kern, H. L. Fehm, J. Born, A. Peters, Modulation of hunger by plasma glucose and metformin, J. Clin. Endocrinol. Metab., 88 (2003), 1133–1141. https://doi.org/10.1210/jc.2002-021450 doi: 10.1210/jc.2002-021450
[83]	B. Schultes, A. Peters, M. Hallschmid, C. Benedict, V. Merl, K. M. Oltmanns, et al., Modulation of food intake by glucose in patients with type 2 diabetes, Diabetes Care, 28 (2005), 2884–2889. https://doi.org/10.2337/diacare.28.12.2884 doi: 10.2337/diacare.28.12.2884
[84]	H. A. J. Gielkens, M. Verkijk, W. F. Lam, C. B. H. W. Lamers, A. A. M. Masclee, Effects of hyperglycemia and hyperinsulinemia on satiety in humans, Metab. Clin. Exp., 47 (1998), 321–324. https://doi.org/10.1016/S0026-0495(98)90264-5 doi: 10.1016/S0026-0495(98)90264-5
[85]	B. Schultes, A.-K. Panknin, M. Hallschmid, K. Jauch-Chara, B. Wilms, F. de Courbière, et al., Glycemic increase induced by intravenous glucose infusion fails to affect hunger, appetite, or satiety following breakfast in healthy men, Appetite, 105 (2016), 562–566. https://doi.org/10.1016/j.appet.2016.06.032 doi: 10.1016/j.appet.2016.06.032
[86]	G. H. Anderson, D. Woodend, Consumption of sugars and the regulation of short-term satiety and food intake, Am. J. Clin. Nut., 78 (2003), 843S–849S. https://doi.org/10.1093/ajcn/78.4.843S doi: 10.1093/ajcn/78.4.843S
[87]	J. M. McMillin, Blood Glucose, Clinical Methods: The History, Physical, and Laboratory Examinations (eds. H. K. Walker, W. D. Hall and J. W. Hurst), 3rd edition. Butterworths, Boston, 1990. URL http://www.ncbi.nlm.nih.gov/books/NBK248/.
[88]	S. J. Russell, F. H. El-Khatib, M. Sinha, K. L. Magyar, K. McKeon, L. G. Goergen, et al., Outpatient glycemic control with a bionic pancreas in type 1 diabetes, N. Engl. J. Med., 371 (2014), 313–325. https://doi.org/10.1056/NEJMoa1314474 doi: 10.1056/NEJMoa1314474
[89]	A. Boutayeb, A. Chetouani, A critical review of mathematical models and data used in diabetology, Biomed. Eng. OnLine., 5 (2006), 43. https://doi.org/10.1186/1475-925X-5-43 doi: 10.1186/1475-925X-5-43
[90]	P. Palumbo, S. Ditlevsen, A. Bertuzzi, A. De Gaetano, Mathematical modeling of the glucose-insulin system: A review, Math. Biosci., 244 (2013), 69–81. https://doi.org/10.1186/1475-925X-5-43 doi: 10.1186/1475-925X-5-43
[91]	A. Mari, A. Tura, E. Grespan, R. Bizzotto, Mathematical modeling for the physiological and clinical investigation of glucose homeostasis and diabetes, Front. Physiol., 11 (2020), 575789. https://doi.org/10.3389/fphys.2020.575789 doi: 10.3389/fphys.2020.575789
[92]	B. Huard, G. Kirkham, Mathematical modelling of glucose dynamics, Curr. Opin. Endocrinol. Metab. Res., 25 (2022), 100379. https://doi.org/10.1016/j.coemr.2022.100379 doi: 10.1016/j.coemr.2022.100379
[93]	R. N. Bergman, G. Bortolan, C. Cobelli, G. Toffolo, Identification of a minimal model of glucose disappearance for estimating insulin sensitivity, IFAC Proc. Vol., 12 (1979), 883–890. https://doi.org/10.1016/S1474-6670(17)65505-8 doi: 10.1016/S1474-6670(17)65505-8
[94]	G. Toffolo, R. N. Bergman, D. T. Finegood, C. R. Bowden, C. Cobelli, Quantitative estimation of beta cell sensitivity to glucose in the intact organism: a minimal model of insulin kinetics in the dog, Diabetes, 29 (1980), 979–990. https://doi.org/10.2337/diab.29.12.979 doi: 10.2337/diab.29.12.979
[95]	A. De Gaetano, O. Arino, Mathematical modelling of the intravenous glucose tolerance test, J. Math. Biol., 40 (2000), 136–168. https://doi.org/10.1007/s002850050007 doi: 10.1007/s002850050007
[96]	S. Panunzi, P. Palumbo, A. De Gaetano, A discrete single delay model for the intra-venous glucose tolerance test, Theor. Biol. Med. Model., 4 (2007), 35. https://doi.org/10.1186/1742-4682-4-35 doi: 10.1186/1742-4682-4-35
[97]	S. Panunzi, A. De Gaetano, G. Mingrone, Advantages of the single delay model for the assessment of insulin sensitivity from the intravenous glucose tolerance test, Theor. Biol. Med. Model., 7 (2010), 9. https://doi.org/10.1186/1742-4682-7-9 doi: 10.1186/1742-4682-7-9
[98]	G. Pacini, R. N. Bergman, MINMOD: a computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test, Comput. Methods Programs Biomed., 23 (1986), 113–122. https://doi.org/10.1016/0169-2607(86)90106-9 doi: 10.1016/0169-2607(86)90106-9
[99]	C. Dalla Man, R. A. Rizza, C. Cobelli, Meal simulation model of the glucose-insulin system, IEEE Trans. Biomed. Eng., 54 (2007), 1740–1749. https://doi.org/10.1109/TBME.2007.893506 doi: 10.1109/TBME.2007.893506
[100]	W. Liu, F. Tang, Modeling a simplified regulatory system of blood glucose at molecular levels, J. Theor. Biol., 252 (2008), 608–620. https://doi.org/10.1016/j.jtbi.2008.02.021 doi: 10.1016/j.jtbi.2008.02.021
[101]	W. Liu, C. Hsin, F. Tang, A molecular mathematical model of glucose mobilization and uptake, Math. Biosci., 221 (2009), 121–129. https://doi.org/10.1016/j.mbs.2009.07.005 doi: 10.1016/j.mbs.2009.07.005
[102]	Z. Wu, C. K. Chui, G. S. Hong, S. Chang, Physiological analysis on oscillatory behavior of glucose–insulin regulation by model with delays, J. Theor. Biol., 280 (2011), 1–9. https://doi.org/10.1016/j.jtbi.2011.03.032 doi: 10.1016/j.jtbi.2011.03.032
[103]	M. Lombarte, M. Lupo, G. Campetelli, M. Basualdo, A. Rigalli, Mathematical model of glucose–insulin homeostasis in healthy rats, Math. Biosci., 245 (2013), 269–277. https://doi.org/10.1016/j.mbs.2013.07.017 doi: 10.1016/j.mbs.2013.07.017
[104]	A. C. Pratt, J. A. D. Wattis, A. M. Salter, Mathematical modelling of hepatic lipid metabolism, Math. Biosci., 262 (2015), 167–181. https://doi.org/10.1016/j.mbs.2014.12.012 doi: 10.1016/j.mbs.2014.12.012
[105]	J. Girard, The incretins: From the concept to their use in the treatment of type 2 diabetes. Part A: incretins: concept and physiological functions, Diabetes Metab., 34 (2008), 550–559. https://doi.org/10.1016/j.diabet.2008.09.001 doi: 10.1016/j.diabet.2008.09.001
[106]	J. J. Holst, C. F. Deacon, T. Vilsbøll, T. Krarup, S. Madsbad, Glucagon-like peptide-1, glucose homeostasis and diabetes, Trends Mol. Med., 14 (2008), 161–168. https://doi.org/10.1016/j.molmed.2008.01.003 doi: 10.1016/j.molmed.2008.01.003
[107]	J. J. Holst, T. Vilsbøll, C. F. Deacon, The incretin system and its role in type 2 diabetes mellitus, Mol. Cell. Endocrinol., 297 (2009), 127–136. https://doi.org/10.1016/j.mce.2008.08.012 doi: 10.1016/j.mce.2008.08.012
[108]	K. Kazakos, Incretin effect: GLP-1, GIP, DPP4, Diabetes Res. Clin. Pract., 93 (2011), S32–S36. https://doi.org/10.1016/S0168-8227(11)70011-0 doi: 10.1016/S0168-8227(11)70011-0
[109]	J. J. Holst, C. F. Deacon, Is there a place for incretin therapies in obesity and prediabetes?, Trends Endocrinol. Metab., 24 (2013), 145–152. https://doi.org/10.1016/j.tem.2013.01.004 doi: 10.1016/j.tem.2013.01.004
[110]	G. Zhao, D. Wirth, I. Schmitz, M. Meyer-Hermann, A mathematical model of the impact of insulin secretion dynamics on selective hepatic insulin resistance, Nat. Commun., 8 (2017), 1–10. https://doi.org/10.1038/s41467-017-01627-9 doi: 10.1038/s41467-017-01627-9
[111]	S. Masroor, M. G. J. van Dongen, R. Alvarez-Jimenez, K. Burggraaf, L. A. Peletier, M. A. Peletier, Mathematical modeling of the glucagon challenge test, J. Pharmacokinet. Pharmacodyn., 46 (2019), 553–564. https://doi.org/10.1007/s10928-019-09655-2 doi: 10.1007/s10928-019-09655-2
[112]	M. C. Palumbo, M. Morettini, P. Tieri, F. Diele, M. Sacchetti, F. Castiglione, Personalizing physical exercise in a computational model of fuel homeostasis, PLoS Comput. Biol., 14 (2018), e1006073. https://doi.org/10.1371/journal.pcbi.1006073 doi: 10.1371/journal.pcbi.1006073
[113]	M. C. Palumbo, A. A. de Graaf, M. Morettini, P. Tieri, S. Krishnan, F. Castiglione, A computational model of the effects of macronutrients absorption and physical exercise on hormonal regulation and metabolic homeostasis, Comput. Biol. Med., 163 (2023), 107158. https://doi.org/10.1016/j.compbiomed.2023.107158 doi: 10.1016/j.compbiomed.2023.107158
[114]	J. Deichmann, S. Bachmann, M. Pfister, G. Szinnai, H.-M. Kaltenbach, A comprehensive model of glucose-insulin regulation including acute and prolonged effects of physical activity in type 1 diabetes, bioRxiv, 2021.06.09.447693. https://doi.org/10.1101/2021.06.09.447693
[115]	N. E. López-Palau, J. M. Olais-Govea, Mathematical model of blood glucose dynamics by emulating the pathophysiology of glucose metabolism in type 2 diabetes mellitus, Sci. Rep., 10 (2020), 12697. https://doi.org/10.1038/s41598-020-69629-0 doi: 10.1038/s41598-020-69629-0
[116]	H. Kurata, Virtual metabolic human dynamic model for pathological analysis and therapy design for diabetes, iScience, 24 (2021), 102101. https://doi.org/10.1016/j.isci.2021.102101 doi: 10.1016/j.isci.2021.102101
[117]	R. N. Bergman, Y. Z. Ider, C. R. Bowden, C. Cobelli, Quantitative estimation of insulin sensitivity., Am. J. Physiol. Endocrinol. Metab., 236 (1979), E667. https://doi.org/10.1152/ajpendo.1979.236.6.E667 doi: 10.1152/ajpendo.1979.236.6.E667
[118]	A. Mukhopadhyay, A. De Gaetano, O. Arino, Modeling the intra-venous glucose tolerance test: a global study for a single-distributed-delay model, DCDS-B, 4 (2004), 407. https://doi.org/10.3934/dcdsb.2004.4.407 doi: 10.3934/dcdsb.2004.4.407
[119]	J. Li, M. Wang, A. De Gaetano, P. Palumbo, S. Panunzi, The range of time delay and the global stability of the equilibrium for an IVGTT model, Math. Biosci., 235 (2012), 128–137. https://doi.org/10.1016/j.mbs.2011.11.005 doi: 10.1016/j.mbs.2011.11.005
[120]	D. V. Giang, Y. Lenbury, A. De Gaetano, P. Palumbo, Delay model of glucose–insulin systems: Global stability and oscillated solutions conditional on delays, J. Math. Anal. Appl., 343 (2008), 996–1006. https://doi.org/10.1016/j.jmaa.2008.02.016 doi: 10.1016/j.jmaa.2008.02.016
[121]	C.-L. Chen, H.-W. Tsai, Modeling the physiological glucose–insulin system on normal and diabetic subjects, Comput. Methods Programs Biomed., 97 (2010), 130–140. https://doi.org/10.1016/j.cmpb.2009.06.005 doi: 10.1016/j.cmpb.2009.06.005
[122]	P. Palumbo, P. Pepe, S. Panunzi, A. De Gaetano, Time-delay model-based control of the glucose-insulin system, by means of a state observer, European J. Control, 6 (2012), 591–606. https://doi.org/10.3166/EJC.18.591-606 doi: 10.3166/EJC.18.591-606
[123]	A. De Gaetano, S. Panunzi, A. Matone, A. Samson, J. Vrbikova, B. Bendlova, et al., Routine OGTT: a robust model including incretin effect for precise identification of insulin sensitivity and secretion in a single individual, PLOS ONE, 8 (2013), e70875. https://doi.org/10.1371/journal.pone.0070875 doi: 10.1371/journal.pone.0070875
[124]	P. Palumbo, G. Pizzichelli, S. Panunzi, P. Pepe, A. De Gaetano, Model-based control of plasma glycemia: Tests on populations of virtual patients, Math. Biosci., 257 (2014), 2–10. https://doi.org/10.1016/j.mbs.2014.09.003 doi: 10.1016/j.mbs.2014.09.003
[125]	U. Picchini, A. De Gaetano, S. Panunzi, S. Ditlevsen, G. Mingrone, A mathematical model of the euglycemic hyperinsulinemic clamp, Theor. Biol. Med. Model., 2 (2005), 44. https://doi.org/10.1186/1742-4682-2-44 doi: 10.1186/1742-4682-2-44
[126]	U. Picchini, S. Ditlevsen, A. De Gaetano, Modeling the euglycemic hyperinsulinemic clamp by stochastic differential equations, J. Math. Biol., 53 (2006), 771–796. https://doi.org/10.1007/s00285-006-0032-z doi: 10.1007/s00285-006-0032-z
[127]	P. Palumbo, A. De Gaetano, An islet population model of the endocrine pancreas, J. Math. Biol., 61 (2010), 171–205. https://doi.org/10.1007/s00285-009-0297-0 doi: 10.1007/s00285-009-0297-0
[128]	A. De Gaetano, C. Gaz, P. Palumbo, S. Panunzi, A unifying organ model of pancreatic insulin secretion, PLOS ONE, 10 (2015), e0142344. https://doi.org/10.1371/journal.pone.0142344 doi: 10.1371/journal.pone.0142344
[129]	A. De Gaetano, C. Gaz, S. Panunzi, Consistency of compact and extended models of glucose-insulin homeostasis: the role of variable pancreatic reserve, PLOS ONE, 14 (2019), e0211331. https://doi.org/10.1371/journal.pone.0211331 doi: 10.1371/journal.pone.0211331
[130]	B. Topp, K. Promislow, G. deVries, R. M. Miura, D. T. Finegood, A model of beta-cell mass, insulin, and glucose kinetics: pathways to diabetes, J. Theor. Biol., 206 (2000), 605–619. https://doi.org/10.1006/jtbi.2000.2150 doi: 10.1006/jtbi.2000.2150
[131]	A. De Gaetano, T. Hardy, B. Beck, E. Abu-Raddad, P. Palumbo, J. Bue-Valleskey, et al., Mathematical models of diabetes progression, Am. J. Physiol. Endocrinol. Metab., 295 (2008), E1462–1479.
[132]	P. C. Fletcher, P. J. Kenny, Food addiction: A valid concept?, Neuropsychopharmacology, 43 (2018), 2506–2513. https://doi.org/10.1038/s41386-018-0203-9 doi: 10.1038/s41386-018-0203-9
[133]	T. Hardy, E. Abu-Raddad, N. Porksen, A. De Gaetano, Evaluation of a mathematical model of diabetes progression against observations in the Diabetes Prevention Program, Am. J. Physiol. Endocrinol. Metab., 303 (2012), E200–E212. https://doi.org/10.1152/ajpendo.00421.2011 doi: 10.1152/ajpendo.00421.2011
[134]	A. De Gaetano, T. A. Hardy, A novel fast-slow model of diabetes progression: Insights into mechanisms of response to the interventions in the diabetes prevention program, PLOS ONE, 14 (2019), e0222833. https://doi.org/10.1371/journal.pone.0222833 doi: 10.1371/journal.pone.0222833
[135]	P. Toghaw, A. Matone, Y. Lenbury, A. De Gaetano, Bariatric surgery and T2dm improvement mechanisms: A mathematical model, Theor. Biol. Med. Model, 9 (2012), 16. https://doi.org/10.1186/1742-4682-9-16 doi: 10.1186/1742-4682-9-16
[136]	C. C. Y. Noguchi, E. Furutani, S. Sumi, Enhanced mathematical model of postprandial glycemic excursion in diabetics using rapid-acting insulin, 2012 SICE AC., 2012,566–571.
[137]	A. De Gaetano, S. Panunzi, D. Eliopoulos, T. Hardy, G. Mingrone, Mathematical modeling of renal tubular glucose absorption after glucose load, PLOS ONE, 9 (2014), e86963, https://doi.org/10.1371/journal.pone.0086963 doi: 10.1371/journal.pone.0086963
[138]	A. Borri, S. Panunzi, A. De Gaetano, A glycemia-structured population model, J. Math. Biol., 73 (2016), 39–62. https://doi.org/10.1007/s00285-015-0935-7 doi: 10.1007/s00285-015-0935-7
[139]	S. Sakulrang, E. J. Moore, S. Sungnul, A. De Gaetano, A fractional differential equation model for continuous glucose monitoring data, Adv. Differ. Equ., 2017 (2017), 150. https://doi.org/10.1186/s13662-017-1207-1 doi: 10.1186/s13662-017-1207-1
[140]	S. Panunzi, A. Borri, L. D'Orsi, A. DeGaetano, Order estimation for a fractional Brownian motion model of glucose control, Commun. Nonlinear Sci. Numer., 127 (2023), 107554. https://doi.org/10.1016/j.cnsns.2023.107554 doi: 10.1016/j.cnsns.2023.107554
[141]	J. Yokrattanasak, A. De Gaetano, S. Panunzi, P. Satiracoo, W. M. Lawton, Y. Lenbury, A simple, realistic stochastic model of gastric emptying, PLoS ONE, 11 (2016). https://doi.org/10.1371/journal.pone.0153297 doi: 10.1371/journal.pone.0153297
[142]	Y. T. Wondmkun, Obesity, insulin resistance, and type 2 diabetes: Associations and therapeutic implications, Diabetes Metab. Syndr. Obes. Targets Ther., 13 (2020), 3611–3616. https://doi.org/10.2147/DMSO.S275898 doi: 10.2147/DMSO.S275898
[143]	B. B. Kahn, J. S. Flier, Obesity and insulin resistance, J. Clin. Invest, 106 (2000), 473–481. https://doi.org/10.1172/JCI10842 doi: 10.1172/JCI10842
[144]	L. Pénicaud, M. F. Kinebanyan, P. Ferré, J. Morin, J. Kandé, C. Smadja, et al., Development of VMH obesity: In vivo insulin secretion and tissue insulin sensitivity, Am. J. Physiol., 257 (1989), E255–260. https://doi.org/10.1152/ajpendo.1989.257.2.E255 doi: 10.1152/ajpendo.1989.257.2.E255
[145]	S. Virtue, A. Vidal-Puig, Adipose tissue expandability, lipotoxicity and the metabolic syndrome–an allostatic perspective, BBA, 1801 (2010), 338–349. https://doi.org/10.1016/j.bbalip.2009.12.006 doi: 10.1016/j.bbalip.2009.12.006
[146]	D. S. Ludwig, C. B. Ebbeling, The carbohydrate-insulin model of obesity: beyond 'calories in, calories out', JAMA Intern. Med., 178 (2018), 1098–1103. https://doi.org/10.1001/jamainternmed.2018.2933 doi: 10.1001/jamainternmed.2018.2933
[147]	R Core Team, R: a Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2023, URL https://www.R-project.org/.
[148]	U. N. UNIVERSITY, Human energy requirements Report of a Joint FAO/WHO/UNU Expert Consultation, 1, 2004.
[149]	A. E. Black, W. A. Coward, T. J. Cole, A. M. Prentice, Human energy expenditure in affluent societies: An analysis of 574 doubly-labelled water measurements, Eur. J. Clin. Nutr., 50 (1996), 72–92.
[150]	M. D. Mifflin, S. T. St Jeor, L. A. Hill, B. J. Scott, S. A. Daugherty, Y. O. Koh, A new predictive equation for resting energy expenditure in healthy individuals, Am. J. Clin. Nutr., 51 (1990), 241–247. https://doi.org/10.1093/ajcn/51.2.241 doi: 10.1093/ajcn/51.2.241

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)