A mathematical model for deciphering the impact of obesity on diabetes

Obesity has emerged as a pressing global issue, with a consistently rising number of affected individuals each year. This alarming trend has led to a cascade of serious health problems, including cancer, heart attacks, and diabetes, among others. The ramifications of obesity extend beyond individual health, affecting economic and social development. Consequently, healthcare professionals must gain a deep understanding of how obesity affects the human body, particularly in terms of its influence on blood sugar levels and the prevention of diabetes. In this research paper, we have formulated a nonlinear model that considers the effect of obesity on plasma glucose concentration, plasma insulin concentration, and β-cell mass. We aim to elucidate the equilibrium points of the model and assess their stability. To account for the impact of β-cell dysfunction, we introduced a time delay in insulin production. We analyze the delay model and calculate the direction of the Hopf bifurcation. The critical Hopf points are calculated analytically for both delay and non-delay models. We have reinforced our findings through a combination of theoretical analysis and numerical simulations. This research explores the dynamics of glucose metabolism to understand how obesity impacts blood sugar levels, providing valuable insights into the broader context of metabolic health.