International Journal of Discrete Mathematics

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Mathematical Analysis of Varicella Zoster Virus Model

Received: 9 July 2021    Accepted: 29 July 2021    Published: 12 October 2021
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Abstract

Chicken Pox (also called Varicella) is a disease caused by a virus known as Varicella Zoster Virus (VZV) also known as human herpes virus 3 (HHV -3). Varicella Zoster Virus (VZV) is a DNA virus of the Herpes group, transmitted by direct contact with infective individuals. In this work, a deterministic mathematical model for transmission dynamics of Varicella Zoster Virus (VZV) with vaccination strategy was solved, using Adomian Decomposition Method (ADM) and Fourth-Fifth Rungekutta Felhberg Method and Approximate solutions were realized. ADM, yields analytical solution in terms of rapidly convergent infinite power series with easily computed terms. This solution was realized by applying Adomian polynomials to the nonlinear terms in the system. Similarly, fourth-fifth-order Runge-Kutta Felberg method with degree four interpolant (RK45F) was used to compute a numerical solution that was used as a reference solution to compare with the semi-analytical approximations. The main advantage of the ADM is that it yields an approximate series solution in close form with accelerated convergence. The effect of Varicella was considered in five compartments: The Susceptible, the Vaccinated, the Exposed, the Infective and the Recovered class. The Varicella Zoster virus model which is a nonlinear system can only be solved conveniently using powerful semi-analytic tool such as the ADM. Numerical simulations of the model show that, the combination of vaccination and treatment is the most effective way to combat the epidemiology of VZV in the community.

DOI 10.11648/j.dmath.20210602.11
Published in International Journal of Discrete Mathematics (Volume 6, Issue 2, December 2021)
Page(s) 23-37
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Varicella, Zoster, Adomian Decomposition, Modeling, Sensitivity, Vaccination, Epidemiology

References
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[2] Dehghan M. and Tatari M., (2006). “The Use of Adomian Decomposition Method for Solving Problems in Calculus of Variations,” Mathematical Problems in Engineering, volume 2006, Article ID 65379, 12 pages.
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[8] Lesnic, D. (2002). Convergence of Adomian's Method: Periodic Temperatures. Applied and Computational Mathematics, 44: 13-24.
[9] John, T. and Edward, J. (1997). A comparison of Adomian Decomposition Methods for Approximate Solution of Some Predator Prey Model Equations Numerical Analysis Report no, 309 a report association with university college chester.
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[18] Edward, Stephen., Dmitry, K. and Silas, M. (2014). Modeling and Stability Analysis for a Varicella Zoster Virus Model with Vaccination. Applied and Computational Mathematics, 3: 150-162.
[19] Gilden, D., Nagel, M., Cohrs, R., Mahalingam, R., and Baird, N. (2015). Varicella zoster virus in the nervous system. F1000Res 4: F1000FacultyRev–1356. doi: 10.12688/f1000research.7153.1.
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[21] Sorel, O., and Messaoudi, I. (2018). Varicella virus-host interactions during latency and reactivation: lessons from simian varicella virus. Front. Microbiol. 9: 3170. doi: 10.3389/fmicb.2018.03170.
[22] Cohrs, R. J., and Gilden, D. H. (2003). Varicella zoster virus transcription in latently-infected human ganglia. Anticancer Res. 23, 2063–2069.
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    Anebi Elisha, Terhemen Aboiyar, Anande Richard Kimbir. (2021). Mathematical Analysis of Varicella Zoster Virus Model. International Journal of Discrete Mathematics, 6(2), 23-37. https://doi.org/10.11648/j.dmath.20210602.11

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    Anebi Elisha; Terhemen Aboiyar; Anande Richard Kimbir. Mathematical Analysis of Varicella Zoster Virus Model. Int. J. Discrete Math. 2021, 6(2), 23-37. doi: 10.11648/j.dmath.20210602.11

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    AMA Style

    Anebi Elisha, Terhemen Aboiyar, Anande Richard Kimbir. Mathematical Analysis of Varicella Zoster Virus Model. Int J Discrete Math. 2021;6(2):23-37. doi: 10.11648/j.dmath.20210602.11

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  • @article{10.11648/j.dmath.20210602.11,
      author = {Anebi Elisha and Terhemen Aboiyar and Anande Richard Kimbir},
      title = {Mathematical Analysis of Varicella Zoster Virus Model},
      journal = {International Journal of Discrete Mathematics},
      volume = {6},
      number = {2},
      pages = {23-37},
      doi = {10.11648/j.dmath.20210602.11},
      url = {https://doi.org/10.11648/j.dmath.20210602.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20210602.11},
      abstract = {Chicken Pox (also called Varicella) is a disease caused by a virus known as Varicella Zoster Virus (VZV) also known as human herpes virus 3 (HHV -3). Varicella Zoster Virus (VZV) is a DNA virus of the Herpes group, transmitted by direct contact with infective individuals. In this work, a deterministic mathematical model for transmission dynamics of Varicella Zoster Virus (VZV) with vaccination strategy was solved, using Adomian Decomposition Method (ADM) and Fourth-Fifth Rungekutta Felhberg Method and Approximate solutions were realized. ADM, yields analytical solution in terms of rapidly convergent infinite power series with easily computed terms. This solution was realized by applying Adomian polynomials to the nonlinear terms in the system. Similarly, fourth-fifth-order Runge-Kutta Felberg method with degree four interpolant (RK45F) was used to compute a numerical solution that was used as a reference solution to compare with the semi-analytical approximations. The main advantage of the ADM is that it yields an approximate series solution in close form with accelerated convergence. The effect of Varicella was considered in five compartments: The Susceptible, the Vaccinated, the Exposed, the Infective and the Recovered class. The Varicella Zoster virus model which is a nonlinear system can only be solved conveniently using powerful semi-analytic tool such as the ADM. Numerical simulations of the model show that, the combination of vaccination and treatment is the most effective way to combat the epidemiology of VZV in the community.},
     year = {2021}
    }
    

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  • TY  - JOUR
    T1  - Mathematical Analysis of Varicella Zoster Virus Model
    AU  - Anebi Elisha
    AU  - Terhemen Aboiyar
    AU  - Anande Richard Kimbir
    Y1  - 2021/10/12
    PY  - 2021
    N1  - https://doi.org/10.11648/j.dmath.20210602.11
    DO  - 10.11648/j.dmath.20210602.11
    T2  - International Journal of Discrete Mathematics
    JF  - International Journal of Discrete Mathematics
    JO  - International Journal of Discrete Mathematics
    SP  - 23
    EP  - 37
    PB  - Science Publishing Group
    SN  - 2578-9252
    UR  - https://doi.org/10.11648/j.dmath.20210602.11
    AB  - Chicken Pox (also called Varicella) is a disease caused by a virus known as Varicella Zoster Virus (VZV) also known as human herpes virus 3 (HHV -3). Varicella Zoster Virus (VZV) is a DNA virus of the Herpes group, transmitted by direct contact with infective individuals. In this work, a deterministic mathematical model for transmission dynamics of Varicella Zoster Virus (VZV) with vaccination strategy was solved, using Adomian Decomposition Method (ADM) and Fourth-Fifth Rungekutta Felhberg Method and Approximate solutions were realized. ADM, yields analytical solution in terms of rapidly convergent infinite power series with easily computed terms. This solution was realized by applying Adomian polynomials to the nonlinear terms in the system. Similarly, fourth-fifth-order Runge-Kutta Felberg method with degree four interpolant (RK45F) was used to compute a numerical solution that was used as a reference solution to compare with the semi-analytical approximations. The main advantage of the ADM is that it yields an approximate series solution in close form with accelerated convergence. The effect of Varicella was considered in five compartments: The Susceptible, the Vaccinated, the Exposed, the Infective and the Recovered class. The Varicella Zoster virus model which is a nonlinear system can only be solved conveniently using powerful semi-analytic tool such as the ADM. Numerical simulations of the model show that, the combination of vaccination and treatment is the most effective way to combat the epidemiology of VZV in the community.
    VL  - 6
    IS  - 2
    ER  - 

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Author Information
  • Mathematics Department, Federal University of Agriculture Makurdi, Makurdi, Nigeria

  • Mathematics Department, Federal University of Agriculture Makurdi, Makurdi, Nigeria

  • Mathematics Department, Federal University of Agriculture Makurdi, Makurdi, Nigeria

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