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

---