Impact of lifestyle interventions and adequate medical infrastructure on diabetes prevention: Dynamics analysis and optimal control

Document Type : Research Article

Authors

Manash Kalita ^{1, 2}

Zenith Mondal ³

Barlin Bhuyan ⁴

Bhagya Jyoti Nath ³

Hemanta Kumar Sarmah ²

¹ Department of Mathematics, Lakhimpur Girls’ College, Lakhimpur 787031, Assam, India.

² Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India.

³ Department of Mathematics, Rabindranath Thakur Vishwavidyalaya, Hojai 782436, Assam, India.

⁴ Department of Mathematics, Mahapurusha Srimanta Sankaradeva Viswavidyalaya, Nagaon 782001, Assam, India.

10.22067/ijnao.2026.97704.1834

Abstract

Diabetes mellitus is a chronic metabolic disorder that affects the ability to regulate blood glucose levels in the human body. In recent decades, the rapid increase in the number of people living with diabetes around the world has made it one of the most pressing public health concerns and places a growing burden on healthcare systems. In this study, we formulate and analyze a non-linear mathematical model to study the effect of lifestyle intervention and proper medical infrastructure on diabetes prevention. We study the basic properties of the model system, like the existence, non-negativity, and boundedness of solutions. Further, a non-trivial equilibrium point for the model system has been found, and local and global stability of the equilibrium point are established. Additionally, we propose an optimal control problem by introducing two control variables that prevent healthy people from becoming pre-diabetic due to a bad lifestyle through spreading awareness about lifestyle intervention and clinical intervention to enhance the treatment rate of the diabetic population with complications. The optimal control problem is further solved to reduce the burden of diabetics with and without complications. Finally, our findings suggest that lifestyle intervention aimed at raising awareness among the healthy population about irregular lifestyles, together with adequate medical infrastructure to improve treatment rates among diabetic individuals with complications, can substantially ease the growing strain imposed by diabetes on healthcare systems.

Keywords

Diabetes

Awareness

Lifestyle intervention

Simulation

Optimal control

Subjects

• Optimal Control

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References

[1] Aljohani, A., Shokri, A. and Mukalazi, H. Analyzing the dynamic patterns of COVID-19
through nonstandard finite difference scheme, Sci. Rep., 14(1) (2024), 8466.
[2] Aljohani, A., Hussain, A. and Shokri, A. Mathematical modeling and the spreading of the
cholera epidemic through numerical methods, Comput. Syst. Oncol., 5(2) (2025), e70006.
[3] Banzi, W., Kambutse, I., Dusabejambo, V., Rutaganda, E., Minani, F., Niyobuhungiro,
J., Mpinganzima, L. and Ntaganda, J.M. Mathematical modelling of glucose–insulin system
and test of abnormalities of type 2 diabetic patients, Int. J. Math. Math. Sci., 2021(1) (2021),
6660177.
[4] Borah, P.B., Nath, B.J., Nath, K.C. and Sarmah, H.K. Stability analysis of a nonlinear
mathematical model for COVID-19 transmission dynamics, Commun. Math. Biol. Neurosci.,
(2023), Article ID 26.
[5] Boutayeb, W., Lamlili, M.E., Boutayeb, A. and Derouich, M. The dynamics of a population
of healthy people, pre-diabetics and diabetics with and without complications with optimal
control, In: Proceedings of the Mediterranean Conference on Information & Communication
Technologies 2015 (MedCT 2015), Vol. 1, Springer Int. Publ., Cham (2016), 463–471.
[6] Chen, Y. and Zhang, J. Dynamic analysis and optimal control of influenza model with
discrete age structure, Math. Methods Appl. Sci., 47(6) (2024), 4260–4282.
[7] Das, P., Das, S., Das, P., Rihan, F.A., Uzuntarla, M. and Ghosh, D. Optimal control strategy
for cancer remission using combinatorial therapy: a mathematical model-based approach,
Chaos Solitons Fractals, 145 (2021), 110789.
[8] Derouich, M., Boutayeb, A., Boutayeb, W. and Lamlili, M. Optimal control approach to the
dynamics of a population of diabetics, Appl. Math. Sci., 8(56) (2014), 2773–2782.
[9] El Mansouri, A., Smouni, I., Khajji, B., Labzai, A., Belam, M. and Tidli, Y. Optimal
control in a mathematical model of a spread of the obesity epidemic and its impact on
diabetes, Commun. Math. Biol. Neurosci., (2023), Article ID 74.
[10] Fleming, W.H. and Rishel, R.W. Deterministic and stochastic optimal control, Springer
Science & Business Media, 2012.
[11] Gupta, R. and Kumar, S. Analysis of fractional-order population model of diabetes and effect
of remission through lifestyle intervention, Int. J. Appl. Comput. Math., 7(2) (2021), 53.
[12] Hallberg, S.J., Gershuni, V.M., Hazbun, T.L. and Athinarayanan, S.J. Reversing type 2
diabetes: a narrative review of the evidence, Nutrients, 11(4) (2019), 766.
[13] Hayes, C. and Kriska, A. Role of physical activity in diabetes management and prevention,
J. Am. Diet. Assoc., 108(4) (2008), S19–S23.
[14] International Diabetes Federation. IDF diabetes atlas, 10th ed., International Diabetes Fed-
eration, Brussels (2021). Available at: https://www.idf.org.
[15] Kouidere, A., Khajji, B., Balatif, O. and Rachik, M. A multi-age mathematical modeling of
the dynamics of population diabetics with effect of lifestyle using optimal control, J. Appl.
Math. Comput., 67(1) (2021), 375–403.
[16] Kouidere, A., Labzai, A., Ferjouchia, H., Balatif, O. and Rachik, M. A new mathematical
modeling with optimal control strategy for the dynamics of population of diabetics and its
complications with effect of behavioral factors, J. Appl. Math., 2020(1) (2020), 1943410.
[17] Kumari, P., Singh, S. and Singh, H.P. Bifurcation and stability analysis of glucose–insulin
regulatory system in the presence of β-cells, Iran. J. Sci. Technol. Trans. A Sci., 45(5) (2021),
1743–1756.
[18] Marín-Peñalver, J.J., Martín-Timón, I., Sevillano-Collantes, C. and del Cañizo-Gómez, F.J.
Update on the treatment of type 2 diabetes mellitus, World J. Diabetes, 7(17) (2016), 354–
395.
[19] Ma, M. and Li, J. Dynamics of a glucose–insulin model, J. Biol. Dyn., 16(1) (2022), 733–745.
[20] Misra, A.K. and Kumari, M. Modeling the effects of TV and social media advertisements
on diabetes, J. Biol. Syst., 31(3) (2023), 1099–1124.
[21] Mollah, S. and Biswas, S. Effect of awareness program on diabetes mellitus: deterministic
and stochastic approach, J. Appl. Math. Comput., 66(1) (2021), 61–86.
[22] Mollah, S. and Biswas, S. Optimal control for the complication of type 2 diabetes: the role
of awareness programs by media and treatment, Int. J. Dyn. Control, 11(2) (2023), 877–891.
[23] Mutyambizi, C., Pavlova, M., Chola, L., Hongoro, C. and Groot, W. Cost of diabetes mellitus
in Africa: a systematic review of existing literature, Glob. Health, 14(1) (2018), 3.
[24] Naik, P.A., Yeolekar, B.M., Owolabi, K.M. and Yeolekar, M. Modeling and analyzing
glucose–insulin interactions during diabetes through fractional dynamics in presence of
glucagon, J. Adv. Res. (2026), accepted.
[25] Nasir, H. Stability analysis and optimal control of a five-state diabetic population model, J.
Stat. Manag. Syst., 25(1) (2022), 245–267.
[26] Nasir, H. Hopf bifurcation analysis for a diabetic population model with two delays and
saturated treatment, Phys. Scr., 96(12) (2021), 125013.
[27] Nath, B.J., Dehingia, K., Mishra, V.N., Chu, Y.M. and Sarmah, H.K. Mathematical analysis
of a within-host model of SARS-CoV-2, Adv. Differ. Equ., 2021(1) (2021), 113.
[28] Nath, B.J., Sarmah, H.K. and Maurer, H. An optimal control strategy for antiretroviral
treatment of HIV infection in presence of immunotherapy, Qual. Theory Dyn. Syst., 21(2)
(2022), 30.
[29] Nath, B.J., Sadri, K., Sarmah, H.K. and Hosseini, K. An optimal combination of antiretro-
viral treatment and immunotherapy for controlling HIV infection, Math. Comput. Simul.,
217 (2024), 226–243.
[30] Ong, K.L., Stafford, L.K., McLaughlin, S.A., Boyko, E.J., Vollset, S.E., Smith, A.E., Dalton,
B.E., Duprey, J., Cruz, J.A., Hagins, H. and Lindstedt, P.A. Global, regional, and national
burden of diabetes from 1990 to 2021, with projections of prevalence to 2050: a systematic
analysis for the Global Burden of Disease Study 2021, Lancet, 402 (2023), 203–234.
[31] Pal, K.K., Rai, R.K., Tiwari, P.K. and Misra, A.K. Mathematical modeling of control mea-
sures for preventing kidney failure and managing diabetes: sensitivity analysis and optimal
strategies, J. Appl. Math. Comput., 71(5) (2025), 6455–6487.
Iran. J. Numer. Anal. Optim., Vol. 16, No. 4, 2026, pp 1366–1400
Kalita, Mondal, Bhuyan, Nath and Sarmah 1400
[32] Pal, K.K., Rai, R.K., Tiwari, P.K. and Misra, A.K. Role of awareness programs on diabetes
prevention and control of viral infection: a study of optimal control, Eur. Phys. J. Plus,
140(2) (2025), 150.
[33] Permatasari, A.H., Tjahjana, R.H. and Udjiani, T. Existence and characterization of optimal
control in mathematics model of diabetics population, J. Phys. Conf. Ser., 983(1) (2018),
012069.
[34] Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V. and Mishchenko, E.F. The mathe-
matical theory of optimal processes, John Wiley & Sons, London, UK (1962).
[35] Rai, R.K., Pal, K.K., Tiwari, P.K., Martcheva, M. and Misra, A.K. Impact of social media
and word-of-mouth on the transmission dynamics of communicable and non-communicable
diseases, Int. J. Biomath., 16 (2024), 2450094.
[36] Urbina, G., Riahi, D.N. and Bhatta, D. Mathematical modeling of nonlinear blood glucose–
insulin dynamics with beta cells effect, Appl. Appl. Math., 15(1) (2020), 10.
[37] World Health Organization. Report of a WHO/IDF consultation, World Health Organization
(2016).
[38] Xu, H.Y., Khalsaraei, M.M., Shokri, A., Ramos, H. and Molayi, M. Nonstandard finite
difference schemes with positivity property with application to a mathematical model of HIV
infection, Appl. Comput. Math., 23(4) (2024), 541–557.
[39] Zhonghua, Z. and Yaohong, S. Qualitative analysis of a SIR epidemic model with saturated
treatment rate, J. Appl. Math. Comput., 34(1) (2010), 177–194.