Numerical Analysis of Varicella Zoster Virus with Vaccination

  • Muhammad Rafiq Department of Mathematics, Faculty of Sciences & Technology, University of Central Punjab, Lahore, Pakistan
  • Zafar Ullah Khan Department of Dermatology, Rashid Latif Medical College Lahore, Pakistan
  • Fazal Dayan Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan.
Keywords: Chickenpox, varicella-zoster-virus, NSFD scheme, Consistency, Vaccination Effect

Abstract

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Chickenpox is caused by varicella-zoster-virus (VZV). VZZ is DNA virus of the group of herpes that is transferred by direct contact with infected individuals. A VZV model is studied in this article. An NSFD scheme is used to obtain the numerical solution of the studied model. The stability and consistency of the developed scheme are discussed. The simulation results are presented. The developed scheme gives reliable estimations in order to describe the studied SVEIR model of VZV.

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References

https://www.who.int/teams/health-product-and-policy-standards/standards-and-specifications/vaccine-standardization/varicella /. (Retrieved on August 01, 2022).

Garnett GP, Grenfell BT. The epidemiology of varicella–zoster virus infections: A mathematical model. Epidemiology & Infection. 1992 Jun;108(3):495-511.

Edmunds, W. J., & Brisson, M. (2002). The effect of vaccination on the epidemiology of varicella zoster virus. Journal of Infection, 44(4), 211-219.

Brisson M, Edmunds WJ, Gay NJ, Law B, De Serres G. Modelling the impact of immunization on the epidemiology of varicella zoster virus. Epidemiology & Infection. 2000 Dec;125(3):651-69.

Forde JE, Meeker B. A model of varicella-zoster reactivation. Mathematical Biosciences & Engineering. 2010;7(4):765.

Edward S, Kuznetsov D, Mirau S. Modeling and stability analysis for a varicella zoster virus model with vaccination. Applied and Computational Mathematics. 2014 Aug 13;3(4):150-62.

Rafiq M, Ahmed N, Rafique M, Ahmad MO. A Reliable Numerical Analysis of Transmission Dynamics of Chicken Pox (Varicella Zoster Virus). Scientific Inquiry and Review. 2020 Dec 31;4(4):31-45.

Elisha A, Aboiyar T, Kimbir AR. Mathematical Analysis of Varicella Zoster Virus Model. Applied and Computational Mathematics. 2021;1(1):10-34.

Qureshi S, Yusuf A, Shaikh AA, Inc M. Transmission dynamics of varicella zoster virus modeled by classical and novel fractional operators using real statistical data. Physica A: Statistical Mechanics and its Applications. 2019 Nov 15;534:122149.

Pillsbury M, Carias C, Samant S, Greenberg D, Pawaskar M. Comparison of performance of varicella vaccines via infectious disease modeling. Vaccine. 2022 May 31.

R. E. Mickens, “A fundamental principle for constructing non-standard finite difference schemes for differential equations,” Journal of Difference Equations and Applications, vol. 11, no. 2, pp. 645–653, 2005.

J. Cresson and F. Pierret, “Nonstandard finite difference schemes preserving dynamical properties,” Journal of Computational and Applied Mathematics, vol. 303, no. 2, pp. 15–30, 2016.

M. Naveed, M. Rafiq, A. Raza, N. Ahmed, I. Khan et al., “Mathematical analysis of novel coronavirus (2019-nCov) delay pandemic model,” Computers, Materials & Continua, vol. 64, no. 3, pp. 1401–1414, 2020.

W. Shatanawi, A. Raza, M. S. Arif, K. Abodayeh, M. Rafiq et al., “An effective numerical method for the solution of a stochastic coronavirus (2019-ncovid) pandemic model,” Computers, Materials & Continua, vol. 66, no. 2, pp. 1121–1137, 2021.

D. Baleanu, S. Zibaei, M. Namjoo and A. Jajarmi, “A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system,” Advances in Difference Equations, vol. 2021, no. 1, pp. 1-19, 2021.

M. T. Hoang, “Reliable approximations for a hepatitis B virus model by nonstandard numerical schemes,” Mathematics and Computers in Simulation, vol. 193, pp. 32-56, 2022.

M. T. Hoang, “Dynamically consistent nonstandard finite difference schemes for a virus-patch dynamic model. Journal of Applied Mathematics and Computing,” 2021. https://doi.org/10.1007/s12190-021-01673-z

K. V. Ratnam, P. Rao and G. Shirisha, “Stability preserving NSFD scheme for a cooperative and supportive network,” International Journal of Dynamics and Control, vol. 9, no. 4, 1576-1588, 2021.

J. Calatayud and M. Jornet, “An improvement of two nonstandard finite difference schemes for two population mathematical models,” Journal of Difference Equations and Applications, vol. 27, no. 3, 422-430, 2021.

Y. O. Tijani and A. R. Appadu, “Unconditionally positive NSFD and classical finite difference schemes for biofilm formation on medical implant using Allen-Cahn equation,” Demonstratio Mathematica, vol. 55, no. 1, pp. 40-60, 2022.

Y. Nawaz, M. S. Arif, W. Shatanawi and M. U. Ashraf, “A new unconditionally stable implicit numerical scheme for fractional diffusive epidemic model,” AIMS Mathematics, vol. 7, no. 8, 14299-14322, 2022.

Ahmad S, Ullah A, Akgül A, Baleanu D. Theoretical and numerical analysis of fractal fractional model of tumor-immune interaction with two different kernels. Alexandria Engineering Journal. 2022 Jul 1;61(7):5735-52.

Akgül A, Inc M, Kilicman A, Baleanu D. A new approach for one-dimensional sine-Gordon equation. Advances in Difference Equations. 2016 Dec;2016(1):1-20.

Modanli M, Akgül A. Numerical solution of fractional telegraph differential equations by theta-method. The European Physical Journal Special Topics. 2017 Dec;226(16):3693-703.

Boutarfa B, Akgül A, Inc M. New approach for the Fornberg–Whitham type equations. Journal of Computational and Applied Mathematics. 2017 Mar 1;312:13-26.

Akgül A, Hashemi MS, Inc M, Raheem SA. Constructing two powerful methods to solve the Thomas–Fermi equation. Nonlinear Dynamics. 2017 Jan;87(2):1435-44.

Arif MS, Raza A, Shatanawi W, Rafiq M, Bibi M. A stochastic numerical analysis for computer virus model with vertical transmission over the internet. Computers, Materials & Continua. 2019 Jan 1;61(3):1025-43.

Shatanawi W, Raza A, Arif MS, Rafiq M, Bibi M, Mohsin M. Essential features preserving dynamics of stochastic Dengue model. Computer Modeling in Engineering & Sciences. 2021 Jan 10;126(1):201-15.

Noor MA, Raza A, Arif MS, Rafiq M, Nisar KS, Khan I, Abdelwahab SF. Non-standard computational analysis of the stochastic COVID-19 pandemic model: An application of computational biology. Alexandria Engineering Journal. 2022 Jan 1;61(1):619-30.

Arif MS, Raza A, Abodayeh K, Rafiq M, Nazeer A. A numerical efficient technique for the solution of susceptible infected recovered epidemic model. Comput. Model. Eng. Sci.. 2020 Jan 1;124(02):477-91.

Alkahtani BS, Koca I. Fractional stochastic sır model. Results in Physics. 2021 May 1;24:104124.

Atangana A, Bonyah E. Fractional stochastic modeling: new approach to capture more heterogeneity. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2019 Jan 17;29(1):013118

Ahmed N, Macías-Díaz JE, Raza A, Baleanu D, Rafiq M, Iqbal Z, Ahmad MO. Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model. Axioms. 2021 Dec 24;11(1):10.

Arif MS, Raza A, Rafiq M, Bibi M, Fayyaz R, Naz M, Javed U. A reliable stochastic numerical analysis for typhoid fever incorporating with protection against infection. Comput. Mater. Continua. 2019 Jan 1;59(3):787-804.

Arenas AJ, Gonzalez-Parra G, Chen-Charpentier BM. Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order. Mathematics and Computers in Simulation. 2016 Mar 1;121:48-63.

Hoang MT, Egbelowo OF. Dynamics of a fractional-order hepatitis b epidemic model and its solutions by nonstandard numerical schemes. InMathematical Modelling and Analysis of Infectious Diseases 2020 (pp. 127-153). Springer, Cham.

Ruhimat QA, Solekhudin I. An Epidemic Model of Varicella with Vaccination. UNEJ e-Proceeding. 2017 Aug 8:351-5.

Published
2022-06-25
How to Cite
1.
Rafiq M, Zafar Ullah Khan, Fazal Dayan. Numerical Analysis of Varicella Zoster Virus with Vaccination. Sci Inquiry Rev. [Internet]. 2022Jun.25 [cited 2024Dec.4];6(2):89-104. Available from: https://journals.umt.edu.pk/index.php/SIR/article/view/2914
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