Title of Paper: Mathematical Analysis of Varicella Zoster Virus Model Authors: Anebi Elisha 1 , T.Aboiyar 2 , A.R. Kimbir 3 Affliliation: Mathematics Statistics and Computer Science Department, College of Sciences, Federal University of Agriculture Makurdi, Nigeria Email address: elidgr8t@gmail.com (Anebi Elisha), taboiyar@gmail.com (T. Aboiyar), anande.kimbir@uam.edu.ng (A.R. Kimbir) To Cite This article: Anebi Elisha, T.Aboiyar, A.R Kimbir. Mathematical Analysis of Varicella Zoster virus. International Journals of Applied and Computational Mathematics. vol. 1, no. 1, 2021, pp.10- 122.doi:10.11648/j.acm.20140101.16 Received: May 18, 2018; Accepted: June 12, 2018; Published: July 04, 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. Keywords: Varicella, Zoster, Adomian Decomposition, Modeling, Sensitivity, Vaccination, Epidemiology 1.0 INTRODUCTION In recent years, a lot of attention has been on the study of the Adomian decomposition method to investigate various scientific models. The ADM method is used for finding the numerical solution of higher-order deferential equations. This method which accurately computes the series solution is of great interest to applied science, engineering, physics, biology, and so forth. The method provides the solution in a rapidly convergent series with components that can be elegantly computed [1]. The work by [2], was aimed at producing approximate solutions which are obtained in rapidly convergent series with elegantly computable components by the Adomian decomposition technique. They also revealed that the Adomian decomposition method is useful for obtaining both a closed form and the explicit solution and numerical approximations of linear or nonlinear differential equations, and it is also quite straight forward to write computer codes. This method has been applied to obtain formal solution to a wide class of stochastic and deterministic problems in science and engineering involving algebraic, diffferential, integrodifferential, differential delay, integral and partial differential equations. It is well known in the literature that the decomposition method provides the solution in a rapidly convergent series where the series may lead to the solution in a closed form if it exists.