Examination of fractional order model for the population of diabetes and the effects of changes in lifestyle on remission

Abstract

Diabetes can always be avoided or controlled by maintaining a balanced diet and exercising regularly. Recent studies have shown that putting a diabetic patient into remission through a strict lifestyle modification programme can help their blood glucose levels return to normal. Nesreen A. et al. introduced a mathematical model of integer order incorporating a Holling type II treatment function. This study extends their work by proposing two fractional-order mathematical models for diabetic individuals, where pre-diabetes progresses to diabetes and remission occurs at moderate-to-severe levels solely through lifestyle changes, without medical treatment. The first fractional model does not include remission, but the second fractional model does. We use the fixed point theorem to show that the suggested diabetes model has a solution. We proceed by considering the stability of the equilibrium point. Further, we employed the Adams-Bashforth-Moulton technique to demonstrate the Type 2 diabetes model’s numerical solution with the help of MATLAB software. Numerical simulation results for a fractional-order Type 2 diabetes model show a clear influence of the derivative’s order and the remission parameters on the diabetic population.

Keywords

• Diabetic population
• fractional derivative operators
• fixed point theorem