A Reliable Numerical Analysis for Stochastic Hepatitis B Virus Epidemic Model with the Migration Effect

  • Muhammad Shoaib ArifEmail author
  • Ali Raza
  • Muhammad Rafiq
  • Mairaj Bibi
Research Paper
Part of the following topical collections:
  1. Mathematics


The dynamics of an infectious disease in a population has a stochastic nature. Considering this stochastic behavior is more desirable when modeling the epidemics. Analyzing a stochastic model gives more insight as compared to its deterministic part only. This work presents a reliable numerical analysis for stochastic hepatitis B virus epidemic model with the migration effect. The outcomes of stochastic hepatitis B model are compared with its corresponding deterministic part. The dynamics of stochastic model is dependent upon a parameter \(H^{*}\), called basic reproductive number. As the value of \(H^{*}\) changes from greater than 1 to less than 1, the dynamics of disease switches from endemic to infection-free state. In this paper, a structure-preserving numerical method is proposed for the analysis of stochastic hepatitis B model. The results obtained using MATLAB programs are compared with existing schemes in the literature which have certain limitations regarding stability and dynamical consistency. The proposed scheme remains stable and consistent for all choices of parameter values.


Hepatitis B virus Stochastic differential equations Stochastic numerical schemes Stochastic NSFD scheme 



We are so thankful to the reviewers for their valuable remarks and suggestions.


No financial support is available for this research article.

Compliance with ethical standards

Conflict of interest

The authors declare they have no conflict of interest.


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Copyright information

© Shiraz University 2019

Authors and Affiliations

  • Muhammad Shoaib Arif
    • 1
    Email author
  • Ali Raza
    • 1
  • Muhammad Rafiq
    • 2
  • Mairaj Bibi
    • 3
  1. 1.Department of MathematicsAir University PAF Complex E-9IslamabadPakistan
  2. 2.Faculty of EngineeringUniversity of Central PunjabLahorePakistan
  3. 3.Department of MathematicsComsats University IslamabadIslamabadPakistan

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