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Modeling the Combined Effect of Hepatitis B Infection and Heavy Alcohol Consumption on the Progression Dynamics of Liver Cirrhosis

Author

Listed:
  • Lemesa Bedjisa Dano
  • Koya Purnachandra Rao
  • Temesgen Duressa Keno

Abstract

Liver cirrhosis is the liver scarring in human body which causes the liver organ failure to function its regular activities effectively and normally. In this paper, we proposed and analyzed the combined effect of hepatitis B virus (HBV) infection and heavy alcohol consumption on the progression dynamics of liver cirrhosis. In order to study the progression dynamics of cirrhosis and to describe the effect of alcohol intake variation on a chronic hepatitis B patients a deterministic model and a logistic function are considered, respectively. The detailed proof of the positivity, boundedness, and biological feasibility of the proposed model is presented. The disease endemic equilibrium point and the existence of bifurcation were investigated in detail. We established and proved the existence theorems for forward and backward bifurcations, respectively. Finally, we performed large scale numerical simulations to verify the analytic work and the result of the numerical simulations reveal that heavy alcohol consumption significantly accelerates the progression of liver cirrhosis in chronic hepatitis B infected individuals.

Suggested Citation

  • Lemesa Bedjisa Dano & Koya Purnachandra Rao & Temesgen Duressa Keno, 2022. "Modeling the Combined Effect of Hepatitis B Infection and Heavy Alcohol Consumption on the Progression Dynamics of Liver Cirrhosis," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:6936396
    DOI: 10.1155/2022/6936396
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    References listed on IDEAS

    as
    1. 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.
    2. Bouchaib Khajji & Abderrahim Labzai & Abdelfatah Kouidere & Omar Balatif & Mostafa Rachik, 2020. "A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control," Journal of Applied Mathematics, Hindawi, vol. 2020, pages 1-13, February.
    3. Bouchaib Khajji & Abderrahim Labzai & Abdelfatah Kouidere & Omar Balatif & Mostafa Rachik, 2020. "A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    4. Bouchaib Khajji & Abderrahim Labzai & Omar Balatif & Mostafa Rachik, 2020. "Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2020, pages 1-12, February.
    5. 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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    Cited by:

    1. Jean Pierre II Kouenkam & Joseph Mbang & Gilbert Chendjou & Herieth Rwezaura & Jean Tchuenche, 2025. "Modeling the Impact of Treatment on Hepatitis B Burden: Mathematical Analysis and Simulation," SN Operations Research Forum, Springer, vol. 6(4), pages 1-74, December.
    2. Fekadu Mosisa Legesse & Koya Purnachandra Rao & Temesgen Duressa Keno, 2023. "Modeling and Optimal Control Analysis Applied to Real Cases of COVID‐19 Pandemic with Double Dose Vaccination in Ethiopia," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    3. Temesgen Duressa Keno & Lemesa Bedjisa Dano & Gamachu Adugna Ganati, 2022. "Optimal Control and Cost‐Effectiveness Strategies of Malaria Transmission with Impact of Climate Variability," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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