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Modeling the Effect of Vaccination and Treatment on the Transmission Dynamics of Hepatitis B Virus and HIV/AIDS Coinfection

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  • Engida Endriyas Endashaw
  • Temesgen Tibebu Mekonnen

Abstract

Hepatitis B and HIV/AIDS coinfections are common globally due to their similar mode of transmission. Since HIV infection modifies the course of HBV infection by increasing the rate of chronicity, prolonging HBV viremia, and increasing liver disease‐associated deaths, individuals with coinfection of both diseases have a higher tendency of developing cirrhosis of the liver, higher levels of HBV DNA, reduced rate of clearance of the hepatitis B e antigen (HBeAg), and more likely to die than an individual with a single infection. This nature of HBV‐HIV/AIDS coinfection motivated us to conduct this study. In this paper, we proposed and rigorously analyzed a deterministic mathematical model with the aim of investigating the effect of vaccination against hepatitis B virus and treatment for all infections on the transmission dynamics of HBV‐HIV/AIDS coinfection in a population. We proved that the solutions of the submodels and the coinfection model are positive and bounded. The models are studied qualitatively using the stability theory of differential equations, and the effective reproduction numbers of the models are derived using the next generation matrix method. Stability of the equilibria of the submodels and the coinfection model is analyzed using Routh‐Hurwitz criteria. The disease‐free and endemic equilibria of the submodels and the coinfection model are computed, and both local and global asymptotic stability conditions for those equilibria are discussed. We performed a sensitivity analysis to illustrate the influence of different parameters on the effective reproduction number of HBV‐HIV/AIDS coinfection model, and we identified the most sensitive parameters are ωB and ωH, which are the effective contact rates for HBV and HIV transmission, respectively. The numerical simulation of the model is done using MATLAB, and the findings from the simulations are discussed. It is observed that if the vaccination and treatment rates are increased, then the number of individuals susceptible to both infections and HBV‐HIV/AIDS coinfection decreases and even falls to zero over time. Hence, it is concluded that vaccination against hepatitis B virus infection, treatment of hepatitis B and HIV/AIDS infections, and HBV‐HIV/AIDS infection at the highest possible rate is very essential to control the spread of HBV‐HIV/AIDS coinfection as an important public health problem.

Suggested Citation

  • Engida Endriyas Endashaw & Temesgen Tibebu Mekonnen, 2022. "Modeling the Effect of Vaccination and Treatment on the Transmission Dynamics of Hepatitis B Virus and HIV/AIDS Coinfection," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnljam:v:2022:y:2022:i:1:n:5246762
    DOI: 10.1155/2022/5246762
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    References listed on IDEAS

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    1. Hasifa Nampala & Matylda Jablonska-Sabuka & Martin Singull, 2021. "Mathematical Analysis of the Role of HIV/HBV Latency in Hepatocytes," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-15, November.
    2. Shewafera Wondimagegnhu Teklu & Temesgen Tibebu Mekonnen, 2021. "HIV/AIDS-Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-21, September.
    3. Shewafera Wondimagegnhu Teklu & Temesgen Tibebu Mekonnen, 2021. "HIV/AIDS‐Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2021(1).
    4. Hasifa Nampala & Matylda Jablonska-Sabuka & Martin Singull, 2021. "Mathematical Analysis of the Role of HIV/HBV Latency in Hepatocytes," Journal of Applied Mathematics, John Wiley & Sons, vol. 2021(1).
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