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

Abstract

In this study, a mathematical model is presented with fractional-order differential equations in the Caputo sense that examines the time-dependent changes of variables representing individuals who are exposed to mobbing, individuals who are not exposed to mobbing, or individuals who gained resistance to mobbing, and individuals who practice mobbing. Existence and uniqueness, and boundedness and non-negativity of the solutions of the proposed model are examined. Additionally, the data set containing the time-dependent changes of these variables has been used as a basis to examine the dynamics in a population. By the data set, the approximate results of 9 different parameters used in the proposed mathematical model with ODE have been found with the lsqcurvefit function. The parameters obtained from the ODE system are rewritten into the proposed fractional model, and the value of the derivative order that gives the minimum error has been investigated. The related Matlab codes are presented in the study. Also, while it is observed that a decrease occurs in the number of individuals exposed to mobbing, there is an increase in the number of individuals who are not exposed to mobbing or who gain resistance to mobbing and individuals who practice mobbing. All the obtained results are shown in graphical detail.