In this paper, a mathematical model is proposed with classical and fractional derivatives to simulate the virus spread that causes Monkey pox disease among rodents and human populations. The model is expressed as a nonlinear system of differential equations by considering the total population as ten compartments. For the current epidemic system, the reproduction number, \(\:\:{R}_{0}\) , is determined using the next-generation matrix technique. Furthermore, the theoretical analysis of the model includes two equilibria, namely endemic and disease-free, which we established using conventional methods and a corresponding stability analysis is performed. The sensitivity analysis is performed to identify the most effective parameters in disease transmission. A parameter fitting method is used to evaluate the model predictions. The observed and predicted cases were found to be in good agreement with minimum error margins. The disease transmission can be controlled by reducing contacts among humans and by limiting growth of rodents. Finally, numerical simulations are presented by utilizing the powerful platform of MATLAB which gives more insight to the system behavior.
