Title: Comparison between pre-diabetes and diabetes model in fuzzy and crisp environment: fuzzy differential equation approach

Authors: Banamali Roy; Animesh Mahata; Hirak Sinha; Balaram Manna

Addresses: Department of Mathematics, Bangabasi Evening College, 19, Rajkumar Chakraborty Sarani, Kolkata-700009, West Bengal, India ' Mahadevnagar High School, Mahadevnagar, Maheshtala, Dist. South 24 Pargana, Kolkata-7000141, West Bengal, India ' Barjuri High School, Bankura, West Bengal, 722169, India ' Sarta Taraknath Institution (H.S.), Paschim Medinipur, West Bengal, 721144, India

Abstract: In this paper we propose a mathematical model for diabetes and pre-diabetes in fuzzy environment. Now due to the presence of fuzzy variable, the model is transformed to a fuzzy differential equation. Now we can use the concept of fuzzy differential equation for solving and stable analysis of the model. Here, after comparing the all-kind solutions of fuzzy and crisp solution of diabetes and pre-diabetes model, we can propose a strong point which is biologically meaningful. The conception of strong fuzzy solution and weak solution of fuzzy diabetes and pre-diabetes model are discussed and suggested which is relevant to this model. Stability criteria have been compared in both cases when fuzzy functions are (i)-gH differentiable and when fuzzy functions are (ii)-gH differentiable. In the point of view of biology, our proposed model system provides strong solution as well as acceptable solution when fuzzy functions are (ii)-gH differentiable. The all results are verified graphically and numerically using MATLAB software.

Keywords: fuzzy differential equation; characterisation theorem; diabetes and pre-diabetes model; stability analysis.

DOI: 10.1504/IJHI.2021.10035134

International Journal of Hybrid Intelligence, 2021 Vol.2 No.1, pp.47 - 66

Received: 01 Jun 2020
Accepted: 27 Jun 2020

Published online: 26 Sep 2021 *

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