Study of fractional order epidemic compartmental model by using artificial deep neural networks

This paper aims to study a compartmental mathematical model of rotavirus disease with fractals fractional order differential equations. In addition, we employ the deep neural networks (DNN) to investigate the aforementioned dynamical system. Recently, DNNs approach has attracted more attention from researchers. The concerned tool has been used very well in investigating various dynamical systems of infectious diseases. This is because the aforementioned field has many applications and is useful in many scientific and engineering research fields. Additionally, a growing number of mathematical methods are being used to study the mathematical modelling of epidemiological diseases. A model that explains the kinetics of rotavirus induced gastroenteritis transmission with vaccinated class is examined in this study. We use the fractal fractional derivative with exponential kernel (FFE) in the Caputo Fabrizio sense. Appropriate results regarding the existence of solutions are obtained for the given model using the traditional fixed point method. The Euler numerical technique is expanded to interpret the results numerically. Several graphical presentations are used to discuss the transmission dynamics of the model under consideration using different fractals fractional orders. Using DNNs technique, we analyze the considered model. One of the algorithms based on Levenberg- Marquardt training algorithm is used in designed DNNs model for the deep learning and training performance. Hence, training, learning and prediction accuracies of the DNNs were examined and verified by using 9 neurons and maximum of 1000 epoches to deduce the regression R, mean square error (MSE) and root mean square error (RMSE). In addition, the predictions deduced from the multilayer artificial DNNs model developed with 9 neurons in the hidden layer have been compared with the numerical results also. The mentioned results have been presented graphically.