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Media coverage campaign in Hepatitis B transmission model

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  • Khan, Muhammad Altaf
  • Islam, Saeed
  • Zaman, Gul

Abstract

In this paper, we consider a transmission model of hepatitis B virus by taking into account media coverage. First, we formulate the model and find the basic reproduction number R0 by using the next generation matrix method. We show that the disease free equilibrium is locally asymptotically stable for R0<1 and unstable if R0>1. We also prove that the system is globally asymptotically stable for R0<1. In order to control the spread of this disease in community, we devise an optimal control problem by introducing three control functions, that is, the educational campaign, vaccination and the media coverage. To do this, we solve analytically the control problem with characterization of control variables using the Portraying’s Maximum Principle. Finally, we present some numerical illustrations.

Suggested Citation

  • Khan, Muhammad Altaf & Islam, Saeed & Zaman, Gul, 2018. "Media coverage campaign in Hepatitis B transmission model," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 378-393.
    • Handle: RePEc:eee:apmaco:v:331:y:2018:i:c:p:378-393
    DOI: 10.1016/j.amc.2018.03.029
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    References listed on IDEAS

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    1. Ebenezer Bonyah & Muhammad Altaf Khan & K O Okosun & Saeed Islam, 2017. "A theoretical model for Zika virus transmission," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-26, October.
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    Cited by:

    1. Ullah, Saif & Khan, Muhammad Altaf, 2020. "Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Alzahrani, E.O. & Khan, M.A., 2018. "Modeling the dynamics of Hepatitis E with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 287-301.
    3. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.
    4. Mbabazi, Fulgensia Kamugisha & Mugisha, J.Y.T. & Kimathi, M., 2018. "Modeling the within-host co-infection of influenza A virus and pneumococcus," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 488-506.
    5. Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "On the analysis of semi-analytical solutions of Hepatitis B epidemic model under the Caputo-Fabrizio operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Shah, Syed Azhar Ali & Khan, Muhammad Altaf & Farooq, Muhammad & Ullah, Saif & Alzahrani, Ebraheem O., 2020. "A fractional order model for Hepatitis B virus with treatment via Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).

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