A mathematical model with fractional order for obesity with positive and negative interactions and its impact on the diagnosis of diabetes

Erick Manuel Delgado Moya; Alain Pietrus; S´everine Bernard; Silvere Paul nuiro

doi:10.33187/jmsm.1339842

EN

A mathematical model with fractional order for obesity with positive and negative interactions and its impact on the diagnosis of diabetes

Abstract

Overweight and obesity are current problems humankind faces and have serious health consequences because they contribute to diseases such as heart diseases and diabetes. In this paper, we present a mathematical model for the study of overweight and obesity in a population and its impact on the growth of the number of diabetics. For the construction of the model, we take into account social factors and the interactions between different elements of society. We use fractional-order derivatives in the Caputo sense because of the advantages of this type of technique with respect to the memory effect, and it shows different behaviors depending on the fractional order. We find the basic reproduction number and prove the local and global stability of the disease-free equilibrium points. We study the sensitivity index with respect to the basic reproduction number for parameters associated with weight gain due to social pressure and the rate of diagnosis of diabetes not associated with body weight. To validate the model, we perform computational simulations with data extracted from the literature. We conclude that for higher fractional orders a higher value of the basic reproduction number was reached. We show that at the end of the study for different fractional orders that normal-weight individuals are decreasing, and overweight, obese, and diabetic people are increasing.

Keywords

Diabetes , Caputo sense , Model , Obesity , Overweight

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Details

Primary Language

English

Subjects

Modelling and Simulation , Applied Mathematics (Other)

Journal Section

Research Article

Authors

Erick Manuel Delgado Moya ^*
0000-0001-5937-5374
Brazil

Alain Pietrus
0009-0005-8064-4950
France

S´everine Bernard
0000-0001-8493-9821
France

Silvere Paul nuiro
0000-0002-9537-7913
France

Early Pub Date

December 7, 2023

Publication Date

December 21, 2023

Submission Date

August 10, 2023

Acceptance Date

November 30, 2023

Published in Issue

Year 2023 Volume: 6 Number: 3

DOI

https://doi.org/10.33187/jmsm.1339842

IZ

https://izlik.org/JA36MS42AJ

APA

Delgado Moya, E. M., Pietrus, A., Bernard, S., & Paul nuiro, S. (2023). A mathematical model with fractional order for obesity with positive and negative interactions and its impact on the diagnosis of diabetes. Journal of Mathematical Sciences and Modelling, 6(3), 133-149. https://doi.org/10.33187/jmsm.1339842

AMA

1.Delgado Moya EM, Pietrus A, Bernard S, Paul nuiro S. A mathematical model with fractional order for obesity with positive and negative interactions and its impact on the diagnosis of diabetes. Journal of Mathematical Sciences and Modelling. 2023;6(3):133-149. doi:10.33187/jmsm.1339842

Chicago

Delgado Moya, Erick Manuel, Alain Pietrus, S´everine Bernard, and Silvere Paul nuiro. 2023. “A Mathematical Model With Fractional Order for Obesity With Positive and Negative Interactions and Its Impact on the Diagnosis of Diabetes”. Journal of Mathematical Sciences and Modelling 6 (3): 133-49. https://doi.org/10.33187/jmsm.1339842.

EndNote

Delgado Moya EM, Pietrus A, Bernard S, Paul nuiro S (December 1, 2023) A mathematical model with fractional order for obesity with positive and negative interactions and its impact on the diagnosis of diabetes. Journal of Mathematical Sciences and Modelling 6 3 133–149.

IEEE

[1]E. M. Delgado Moya, A. Pietrus, S. Bernard, and S. Paul nuiro, “A mathematical model with fractional order for obesity with positive and negative interactions and its impact on the diagnosis of diabetes”, Journal of Mathematical Sciences and Modelling, vol. 6, no. 3, pp. 133–149, Dec. 2023, doi: 10.33187/jmsm.1339842.

ISNAD

Delgado Moya, Erick Manuel - Pietrus, Alain - Bernard, S´everine - Paul nuiro, Silvere. “A Mathematical Model With Fractional Order for Obesity With Positive and Negative Interactions and Its Impact on the Diagnosis of Diabetes”. Journal of Mathematical Sciences and Modelling 6/3 (December 1, 2023): 133-149. https://doi.org/10.33187/jmsm.1339842.

JAMA

1.Delgado Moya EM, Pietrus A, Bernard S, Paul nuiro S. A mathematical model with fractional order for obesity with positive and negative interactions and its impact on the diagnosis of diabetes. Journal of Mathematical Sciences and Modelling. 2023;6:133–149.

MLA

Delgado Moya, Erick Manuel, et al. “A Mathematical Model With Fractional Order for Obesity With Positive and Negative Interactions and Its Impact on the Diagnosis of Diabetes”. Journal of Mathematical Sciences and Modelling, vol. 6, no. 3, Dec. 2023, pp. 133-49, doi:10.33187/jmsm.1339842.

Vancouver

1.Erick Manuel Delgado Moya, Alain Pietrus, S´everine Bernard, Silvere Paul nuiro. A mathematical model with fractional order for obesity with positive and negative interactions and its impact on the diagnosis of diabetes. Journal of Mathematical Sciences and Modelling. 2023 Dec. 1;6(3):133-49. doi:10.33187/jmsm.1339842