A Neural Study of the Fractional Heroin Epidemic Model

Abstract

This works intends to provide numerical solutions based on the nonlinear fractional order derivatives of the classical White and Comiskey model (NFD-WCM). The fractional order derivatives have provided authentic and accurate solutions for the NDF-WCM. The solutions of the fractional NFD-WCM are provided using the stochastic computing supervised algorithm named Levenberg-Marquard Backpropagation (LMB) based on neural networks (NNs). This regression approach combines gradient descent and Gauss-Newton iterative methods, which means finding a solution through the sequences of different calculations. WCM is used to demonstrate the heroin epidemics. Heroin has been on-growth world wide, mainly in Asia, Europe, and the USA. It is the fourth foremost cause of death due to taking an overdose in the USA. The nonlinear mathematical system NFD-WCM discusses the overall circumstance of different drug users, such as suspected groups, drug users without treatment, and drug users with treatment. The numerical results of NFD-WCM via LMB-NNs have been substantiated through training, testing, and validation measures. The stability and accuracy are then checked through the statistical tool, such as mean square error (MSE), error histogram, and fitness curves. The suggested methodology's strength is demonstrated by the high convergence between the reference solutions and the solutions generated by adding the efficacy of a constructed solver LMB-NNs, with accuracy levels ranging from 10 −9 to 10 −10 .