### Mathematical Analysis of Varicella Zoster Virus Model

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

 Published in International Journal of Discrete Mathematics (Volume 6, Issue 2) DOI 10.11648/j.dmath.20210602.11 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), 2021. Published by Science Publishing Group
Keywords

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

References
• APA Style

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

ACS 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

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

• ```@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}
}
```
• ```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  - ```
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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