Application of Fractional $SPR$ Psychological Disease Model in Turkey and Stability Analysis

Zafer Öztürk; Halis Bilgil; Sezer Sorgun

doi:10.33187/jmsm.1196961

EN

Application of Fractional $SPR$ Psychological Disease Model in Turkey and Stability Analysis

Abstract

Psychological diseases and their treatment are problems related to public health. According to data from the World Health Organization, about a billion people have either mental illness or substance use disorder problems in 2017. Mental, neurological diseases and substance use disorders account for 30 percent of the global non-fatal disease burden and 10 percent of the global disease burden. It is noted that in the world Dec 2005 and 2015, the incidence of mental health diseases increased by about 16 percent. In this study, we have created a fractional-order mathematical modeling for the population of individuals suering from psychological diseases in a society. In this model, the total population was divided into three compartments: individuals who did not receive psychological treatment (S), individuals who received psychological support (P) and individuals who recovered after completing psychological treatment (R). As a fractional derivative, we used the Caputo derivative definitions. Numerical solutions were obtained with the help of Euler method by performing stability analysis related to the fractional SPR model created for the mathematical model of psychological patients. Thus, it was interpreted by creating dynamics for the number of individuals with psychological problems in a population.

Keywords

Fractional Psychological Disease Model, Mathematical Modeling, Euler Method, Caputo Derivative, Stability analysis.

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Zafer Öztürk ^*
0000-0001-5662-4670
Türkiye

Halis Bilgil
0000-0002-8329-5806
Türkiye

Sezer Sorgun
0000-0001-8708-1226
Türkiye

Publication Date

August 7, 2023

Submission Date

October 31, 2022

Acceptance Date

December 31, 2022

Published in Issue

Year 2023 Volume: 6 Number: 2

DOI

https://doi.org/10.33187/jmsm.1196961

IZ

https://izlik.org/JA99WN72LD

APA

Öztürk, Z., Bilgil, H., & Sorgun, S. (2023). Application of Fractional $SPR$ Psychological Disease Model in Turkey and Stability Analysis. Journal of Mathematical Sciences and Modelling, 6(2), 49-55. https://doi.org/10.33187/jmsm.1196961

AMA

1.Öztürk Z, Bilgil H, Sorgun S. Application of Fractional $SPR$ Psychological Disease Model in Turkey and Stability Analysis. Journal of Mathematical Sciences and Modelling. 2023;6(2):49-55. doi:10.33187/jmsm.1196961

Chicago

Öztürk, Zafer, Halis Bilgil, and Sezer Sorgun. 2023. “Application of Fractional $SPR$ Psychological Disease Model in Turkey and Stability Analysis”. Journal of Mathematical Sciences and Modelling 6 (2): 49-55. https://doi.org/10.33187/jmsm.1196961.

EndNote

Öztürk Z, Bilgil H, Sorgun S (August 1, 2023) Application of Fractional $SPR$ Psychological Disease Model in Turkey and Stability Analysis. Journal of Mathematical Sciences and Modelling 6 2 49–55.

IEEE

[1]Z. Öztürk, H. Bilgil, and S. Sorgun, “Application of Fractional $SPR$ Psychological Disease Model in Turkey and Stability Analysis”, Journal of Mathematical Sciences and Modelling, vol. 6, no. 2, pp. 49–55, Aug. 2023, doi: 10.33187/jmsm.1196961.

ISNAD

Öztürk, Zafer - Bilgil, Halis - Sorgun, Sezer. “Application of Fractional $SPR$ Psychological Disease Model in Turkey and Stability Analysis”. Journal of Mathematical Sciences and Modelling 6/2 (August 1, 2023): 49-55. https://doi.org/10.33187/jmsm.1196961.

JAMA

1.Öztürk Z, Bilgil H, Sorgun S. Application of Fractional $SPR$ Psychological Disease Model in Turkey and Stability Analysis. Journal of Mathematical Sciences and Modelling. 2023;6:49–55.

MLA

Öztürk, Zafer, et al. “Application of Fractional $SPR$ Psychological Disease Model in Turkey and Stability Analysis”. Journal of Mathematical Sciences and Modelling, vol. 6, no. 2, Aug. 2023, pp. 49-55, doi:10.33187/jmsm.1196961.

Vancouver

1.Zafer Öztürk, Halis Bilgil, Sezer Sorgun. Application of Fractional $SPR$ Psychological Disease Model in Turkey and Stability Analysis. Journal of Mathematical Sciences and Modelling. 2023 Aug. 1;6(2):49-55. doi:10.33187/jmsm.1196961