Using Deep Neural Network and Fractional Derivative to Investigate Evolution of Virulence

This manuscript is related to investigating a mathematical model for the evolution of virulence by using Deep Neural Networks (DNNs) and fractional order derivative with powerlaw kernel. Sufficient conditions are deduced for the existence and uniqueness of solution to the mentioned model. For the required results, fixed point theory is used. Also, some conditions related to local and global stability are established. Sensitivity analysis has also studied by using the direct method for the computed reproductive number. For the numerical analysis, we use the Euler’s numerical tool. Further, DNNs is used to classify some probabilistic results including Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and regression coefficient. We use the Levenberg-Marquardt algorithm to simulate the results. Several graphical illustrations have been given to to demonstrate the evolution process by using different values for fractional orders. Also, for all compartments, we have elaborated different graphical illustration to highlight the applicability of DNNs.