Fractional Mathematical Modeling of the Mumps, Encephalitis, Pancreatitis with Real Data from Romania and Bifurcation Analysis

In this study, we are considering the mathematical modeling of mumps disease in six subclasses. To investigate the transmission, spread and subsequent transformation of mumps disease into encephalitis and pancreatitis diseases, we name these subclasses as follows: susceptible individuals, vaccinated individuals, infected individuals, recovered individuals, individuals with encephalitis and individuals with pancreatitis. These classes are indicated, respectively, as follows: susceptible individuals [Formula: see text], vaccinated individuals [Formula: see text], infected individuals [Formula: see text], recovered individuals [Formula: see text], encephalitis individuals [Formula: see text] and pancreatitis individuals [Formula: see text] and total population [Formula: see text]. The dynamic behavior of the system has been studied through numerical simulations. To determine whether the proposed model fits the actual data, we calculated the parameters of the model using the least squares curve fitting method (LSCFM). The values of the parameters have been estimated from the actual mumps data from Romania. When the graphs have been examined, it is seen that they were compatible with the biological course of mumps disease because real data have been used. Later, we observed the changes that occur in susceptible, vaccinated, infected, recovered individuals, encephalitis individuals and pancreatitis individuals when we change the values of some parameters. Thus, it is desired to contribute to the prevention of infectious mumps disease by using a mathematical modeling.