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Modeling and control of the hepatitis B virus spreading using an epidemic model

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  • Khan, Tahir
  • Ullah, Zakir
  • Ali, Nigar
  • Zaman, Gul

Abstract

We describe the formulation of hepatitis B epidemic model with saturated incidence rate. Once we formulate the epidemic problem then we discuss the basic properties (existence of positive solutions and positively invariant set etc.) to show the mathematical as well as the biological feasibility. We find the basic reproduction number R0. The disease free and endemic equilibria of the model will be obtained to investigate the local stability and backward bifurcation. We also perform the local sensitivity analysis and find the sensitive parameter. On the basis of this, we develop the optimal control strategy for the elimination of hepatitis B virus (HBV) spreading with the help of optimization theory. Finally, a large scale numerical simulation will be performed to verify our analytical findings.

Suggested Citation

  • Khan, Tahir & Ullah, Zakir & Ali, Nigar & Zaman, Gul, 2019. "Modeling and control of the hepatitis B virus spreading using an epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 1-9.
    • Handle: RePEc:eee:chsofr:v:124:y:2019:i:c:p:1-9
    DOI: 10.1016/j.chaos.2019.04.033
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    References listed on IDEAS

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    1. Parsamanesh, Mahmood & Erfanian, Majid, 2018. "Global dynamics of an epidemic model with standard incidence rate and vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 192-199.
    2. Kabir, K.M. Ariful & Kuga, Kazuki & Tanimoto, Jun, 2019. "Analysis of SIR epidemic model with information spreading of awareness," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 118-125.
    3. Tilahun, Getachew Teshome & Makinde, Oluwole Daniel & Malonza, David, 2018. "Co-dynamics of Pneumonia and Typhoid fever diseases with cost effective optimal control analysis," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 438-459.
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    Cited by:

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    2. Din, Anwarud & Li, Yongjin & Khan, Tahir & Zaman, Gul, 2020. "Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. Juhui Yan & Wanqin Wu & Qing Miao & Xuewen Tan, 2024. "Global Dynamics and Optimal Control of a Fractional-Order SIV Epidemic Model with Nonmonotonic Occurrence Rate," Mathematics, MDPI, vol. 12(17), pages 1-21, September.
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    5. Tingting Xue & Xiaolin Fan & Yan Xu, 2023. "Kinetic Behavior and Optimal Control of a Fractional-Order Hepatitis B Model," Mathematics, MDPI, vol. 11(17), pages 1-18, August.
    6. Rana Yousif & Aref Jeribi & Saad Al-Azzawi, 2023. "Fractional-Order SEIRD Model for Global COVID-19 Outbreak," Mathematics, MDPI, vol. 11(4), pages 1-19, February.
    7. Hoang, Manh Tuan, 2023. "Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 291-314.
    8. Fatima, Bibi & Zaman, Gul, 2020. "Co-infection of Middle Eastern respiratory syndrome coronavirus and pulmonary tuberculosis," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Jorge E. Macías-Díaz & Nauman Ahmed & Muhammad Rafiq, 2019. "Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model," Mathematics, MDPI, vol. 7(12), pages 1-16, December.

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