A Neural Study of the Fractional Heroin Epidemic Model

Wajaree Weera, Thongchai Botmart, Samina Zuhra, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Salem Ben Said

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)4453-4467
Number of pages15
JournalComputers, Materials and Continua
Issue number2
Publication statusPublished - 2023


  • Fractional order
  • heroin epidemic mathematical system
  • neural networks
  • numerical results
  • white-comiskey model

ASJC Scopus subject areas

  • Biomaterials
  • Modelling and Simulation
  • Mechanics of Materials
  • Computer Science Applications
  • Electrical and Electronic Engineering


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