A compartmental fractional-order mobbing model and the determination of its parameters

Işık E., Daşbaşı B.

Bulletin of Biomathematics (BBM), vol.1, no.2, pp.153-176, 2023 (Peer-Reviewed Journal)


In this study, a mathematical model is presented with fractional-order differential equations in theCaputo sense that examines the time-dependent changes of variables representing individuals whoare exposed to mobbing, individuals who are not exposed to mobbing, or individuals who gainedresistance to mobbing, and individuals who practice mobbing. Existence and uniqueness, and bound-edness and non-negativity of the solutions of the proposed model are examined. Additionally, thedata set containing the time-dependent changes of these variables has been used as a basis to examinethe dynamics in a population. By the data set, the approximate results of 9 different parameters usedin the proposed mathematical model with ODE have been found with thelsqcurvefitfunction. Theparameters obtained from the ODE system are rewritten into the proposed fractional model, and thevalue of the derivative order that gives the minimum error has been investigated. The related Matlabcodes are presented in the study. Also, while it is observed that a decrease occurs in the numberof individuals exposed to mobbing, there is an increase in the number of individuals who are notexposed to mobbing or who gain resistance to mobbing and individuals who practice mobbing. Allthe obtained results are shown in graphical detail.