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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Effect of Medication in a Glucose-Insulin Mathematical Model

Journal of Applied Nonlinear Dynamics 13(4) (2024) 795--803 | DOI:10.5890/JAND.2024.12.012

Evandro G. Seifert$^1$, Jos\'e Trobia$^2$, F\'atima E. Cruziniani$^{1,2}$, Diogo L. M. de Souza$^1$, Elaheh Sayari$^1$, Enrique C. Gabrick$^1$, Kelly C. Iarosz$^{1,3,4}$, Jos\'e D. Szezech Jr$^{1,2}$, Iber\^e L. Caldas$^4$,\\ Antonio M. Batista$^{1,2,4}$

$^1$ Graduate Program in Sciences, State University of Ponta Grossa, 84030-900, Ponta Grossa, PR, Brazil

$^2$ Department of Mathematics and Statistics, State University of Ponta Grossa, 84030-900, Ponta Grossa, PR, Brazil

$^3$ University Center UNIFATEB, 84266-010, Tel^emaco Borba, PR, Brazil

$^4$ Physics Institute, University of S~ao Paulo, 05508-900, S~ao Paulo, SP, Brazil

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Abstract

Insulin is a hormone that plays a crucial role in regulating the blood glucose. It is secreted by the beta cells of the pancreas. A chronic disease, known as diabetes, occurs when there is no effective use or no enough secretion of insulin. The treatment, such as insulin injections and medicines, depends on the type of diabetes. Mathematical models have been proposed to understand the dynamics of the glucose-insulin regulatory system in different conditions. In this work, we investigate a model that describes the dynamics of the glucose and insulin concentrations with beta cells. We introduce the effect of medication in a glucose-insulin model. It is analysed a treatment with continuous medication and another with discontinuity in the drug use. We identify parameter values related to medicines that maintain the blood glucose concentration in a normal level.

Acknowledgments

This work was possible by partial financial support from the following Brazilian government agencies: Funda\c c\~ao Arauc\'aria, CNPq (311168/2020-5, 350073/2022-8), CAPES, and S\~ao Paulo Research Foundation (FAPESP 2018/03211-6, 2022/13761-9). We would like to thank 105 Group Science\\ (www.105groupscience.com).

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