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Mathematical modeling of diabetes and its restrain

Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamilnadu, India

E-mail Address: [email protected]

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and

S. Athithan

Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamilnadu, India

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S012918312150114XCited by:3 (Source: Crossref)

Abstract

In this paper, we have developed a mathematical model of diabetes (type-2 diabetes) in a deterministic approach. We have described our model in the population dynamics with four compartments. Namely, Susceptible, Imbalance Glucose Level (IGL), Treatment and Restrain population. Our model exhibits two nonnegative equilibrium points namely Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The expression for the Treatment reproduction number $R_{T}$ is computed. We have proved that the equilibrium points of the model are locally and globally asymptotically stable under some conditions. Numerical simulation is performed to verify our analytical findings such as stability of DFE and EE. The simulations show better results based on the required conditions. We tried to fit our model with the data given by the International Diabetes Federation (IDF) [D. Atlas, IDF Diabetes Atlas, 8th edn. (International Diabetes Federation, Brussels, Belgium, 2017)] and it suits well with the data. It has been found that our model shows the decrease in diabetes-affected population compared with the data given by the IDF [D. Atlas, IDF Diabetes Atlas, 8th edn. (International Diabetes Federation, Brussels, Belgium, 2017)].

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