Mathematical model for the study of obesity in a population and its impact on the growth of diabetes
Abstract
In this paper, we present a deterministic mathematical model for the study of overweight, and obesity in a population and its impact on the growth of the number of diabetics. For the construction of the model, we take into account social factors and the interactions between the elements of society. We find the basic reproduction number and prove the global stability of the disease-free equilibrium point. We present theoretical results and find the sensitivity indices to characterize the impact of parameters associated with overweight, obesity and diagnosed diabetes on the basic reproduction number. To validate the model, we perform computational simulations and study the basic reproduction number and compartments. We present the behavior of the compartments for a scenario and study the impact of the variation of parameters associated with overweight by social pressure and diabetes due to causes other than obesity.
Keyword : diabetes, obesity, overweight, mathematical model, ordinary differential equation
How to Cite
Delgado Moya, E., Pietrus, A., & Bernard, S. (2023). Mathematical model for the study of obesity in a population and its impact on the growth of diabetes. Mathematical Modelling and Analysis, 28(4), 611–635. https://doi.org/10.3846/mma.2023.17510
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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C.M.A. Pinto and A.R.M. Carvalho. The HIV/TB coinfection severity in the presence of TB multi-drug resistant strains. Ecological Complexity, 32(Part A):1– 20, 2019. https://doi.org/10.1016/j.ecocom.2017.08.001
Sandhya and D. Kumar. Mathematical model for glucose-insulin regulatory system of diabetes mellitus. Advances in Applied Mathematical Biosciences, 2(1):39–46, 2011.
W. Wang. Mathematical analysis of an obesity model with eating behaviors. CSIAM Transactions on Applied Mathematics, 1(2):240–255, 2020. https://doi.org/10.4208/csiam-am.2020-0007
T. Yang, B. Zhao and D. Pei. Evaluation of the association between obesity markers and type 2 diabetes: A cohort study based on a physical examination population. Journal of Diabetes Research PB-Hindawi, p. 6503339, 2021. https://doi.org/10.1155/2021/6503339
M. Zamir, G. Zaman and A.S. Alshomrani. Sensitivity analysis and optimal control of anthroponotic cutaneous leishmania. PLoS ONE, 11(8):e0160513, 2016. https://doi.org/10.1371/journal.pone.0160513
S.M. Al-Tuwairqi and R.T. Matbouli. Modeling dynamics of fast food and obesity for evaluating the peer pressure effect and workout impact. Advances in Difference Equations, 59(2021):1–22, 2021. https://doi.org/10.1186/s13662-021-03217-y
H. Al Ali, A. Daneshkhah, A. Boutayeb and Z. Mukandavire. Examining type 1 diabetes mathematical models using experimental data. Int. J. Environ. Res. Public Health, 19:737–757, 2022. https://doi.org/10.3390/ijerph19020737
S. Anusha and S. Athithan. Mathematical modeling of diabetes and its restrain. International Journal of Modern Physics C (IJMPC), 32(9):2150114, 2021. https://doi.org/10.1142/S012918312150114X
W. Banzi, I. Kambutse, V. Dusabejambo, E. Rutaganda, F. Minani, J. Niyobuhungiro, L. Mpinganzima and J.M. Ntaganda. Mathematical modelling of glucose-insulin system and test of abnormalities of type 2 diabetic patients. International Journal of Mathematics and Mathematical Sciences, p. 6660177, 2021. https://doi.org/10.1155/2021/6660177
S. Bernard, T. Cesar and A. Pietrus. The impact of media coverage on obesity. Contemporary Mathematics, 3(1):60–71, 2022. https://doi.org/10.37256/cm.3120221199
C. Castillo-Chavez, Z. Feng and W. Huang. On the computation of R0 and its role on global stability. In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, Springer-Verlag, New York, pp. 229–250, 2002.
N. Chitnis, J.M. Hyman and J.M. Cushing. Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bulletin of Mathematical Biology, 70(5):1272–1296, 2008. https://doi.org/10.1007/s11538-008-9299-0
O. Diekmann, J.A.P. Heesterbeek and J.A.J. Metz. On the definition and the computation of the basic reproduction ratio in model for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28:365–382, 1990. https://doi.org/10.1007/BF00178324
O. Diekmann, J.A.P. Heesterbeek and M.G. Roberts. The construction of nextgeneration matrices for compartmental epidemic models. J. R. Soc. Interface, 7(47):873–85, 2010. https://doi.org/10.1098/rsif.2009.0386
P. Van Den Driessche and J. Watmough. Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180:29–48, 2002. https://doi.org/10.1016/s0025-5564(02)00108-6
R.S. Dubey and P. Goswami. Mathematical model of diabetes and its complications involving fractional operator without singular kernel. Discrete and Continuous Dynamical Systems Series S, 14(7):2151–2161, 2021. https://doi.org/10.3934/dcdss.2020144
K. Ejima, D. Thomas and D.B. Allison. A mathematical model for predicting obesity transmission with both genetic and nongenetic heredity. Obesity (Silver Spring, 26(5):927–933, 2018. https://doi.org/10.1002/oby.22135
Centers for Disease Control and Prevention. About Underlying Cause of Death 1999–2019. CDC WONDER Online Database, 2019 [cited 21 March 2022]. Available on Internet: http://wonder.cdc.gov/ucd-icd10.html
Centers for Disease Control and Prevention. National Diabetes Statistics Report, 2020 [cited 22 March 2022]. Available on Internet: https://www.cdc.gov/diabetes/pdfs/data/statistics/national-diabetes-statistics-report.pdf
A. Golay and J. Ybarra. Link between obesity and type 2 diabetes. Best Pract Res Clin Endocrinol Metab, 19(4):649–663, 2005. https://doi.org/10.1016/j.beem.2005.07.010
S. Kim and So-Yeun Kim. Mathematical modeling for the obesity dynamics with psychological and social factors. East Asian Math. J., 34(3):317–330, 2018. https://doi.org/10.7858/eamj.2018.023
E.M.D. Moya, A. Pietrus and S.M. Oliva. Mathematical model with fractional order derivatives for tuberculosis taking into account its relationship with HIV/AIDS and diabetes. Jambura Journal of Biomathematics, 2(2):80–95, 2021. https://doi.org/10.34312/jjbm.v2i2.11553
F.N. Ngoteya and Y. Nkansah-Gyekye. Sensitivity analysis of parameters in a competition model. Applied and Computational Mathematics, 4(5):363–368, 2015. https://doi.org/10.11648/j.acm.20150405.15
F.Q. Nuttall. Body mass index: Obesity, bmi, and health: A critical review. Nutrition Research, 50(3):117–128, 2015. https://doi.org/10.1097/NT.0000000000000092
World Health Organization. Obesity and overweight, 2021 [cited 23 March 2022]. Available on Internet: https://www.who.int/news-room/fact-sheets/detail/obesity-and-overweight
L.P. Paudel. Mathematical modeling on the obesity dynamics in the southeastern region and the effect of intervention. Universal Journal of Applied Mathematics, 7(3):41–52, 2019. https://doi.org/10.13189/ujam.2019.070302
C.M.A. Pinto and A.R.M. Carvalho. Diabetes mellitus and TB co-existence: Clinical implications from a fractional order modelling. Applied Mathematical Modelling, 68:219–243, 2019. https://doi.org/10.1016/j.apm.2018.11.029
C.M.A. Pinto and A.R.M. Carvalho. The HIV/TB coinfection severity in the presence of TB multi-drug resistant strains. Ecological Complexity, 32(Part A):1– 20, 2019. https://doi.org/10.1016/j.ecocom.2017.08.001
Sandhya and D. Kumar. Mathematical model for glucose-insulin regulatory system of diabetes mellitus. Advances in Applied Mathematical Biosciences, 2(1):39–46, 2011.
W. Wang. Mathematical analysis of an obesity model with eating behaviors. CSIAM Transactions on Applied Mathematics, 1(2):240–255, 2020. https://doi.org/10.4208/csiam-am.2020-0007
T. Yang, B. Zhao and D. Pei. Evaluation of the association between obesity markers and type 2 diabetes: A cohort study based on a physical examination population. Journal of Diabetes Research PB-Hindawi, p. 6503339, 2021. https://doi.org/10.1155/2021/6503339
M. Zamir, G. Zaman and A.S. Alshomrani. Sensitivity analysis and optimal control of anthroponotic cutaneous leishmania. PLoS ONE, 11(8):e0160513, 2016. https://doi.org/10.1371/journal.pone.0160513