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

Öztürk Z., Bilgil H., Sorgun S.

Journal of mathematical sciences and modelling (Online), vol.6, no.2, pp.49-55, 2023 (Scopus)


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 of the population of individuals suffering 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 the 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.