A Reliable Numerical Analysis of Transmission Dynamics of Chicken Pox (Varicella Zoster Virus)

  • Muhammad Rafiq Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, Pakistan
  • Nauman Ahmed Department of Mathematics & Statistics, Minhaj University, Lahore, Pakistan
  • Mudassar Rafique Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
  • Muhammad Ozair Ahmad Department of Mathematics & Statistics, Minhaj University, Lahore, Pakistan
Keywords: convergence, epidemiology, mathematical modeling, Non-Standard Finite Difference (NSFD) method, sensitivity, treatment, vaccination, Varicella Zoster

Abstract

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Solutions generated through numerical techniques are great in solving real-world problems. This manuscript deals with the numerical approximation of the epidemic system, describing the transmission dynamics of the Vercilla Zoster Virus (VZV) through the impact of vaccination. To discretize the continuous dynamical system, we proposed a novel numerical technique that preserves the true dynamics of the VZV epidemic model. The proposed technique is established in such a manner that it sustains all necessary physical traits depicted by the epidemic model under study. The designed technique is named a nonstandard finite difference (NSFD) scheme. Theoretical analysis of the designed NSFD technique is presented which describes its strength over the standard numerical procedures which are already being used for such purposes. The graphical solutions of all the numerical techniques are presented which verify the efficacy of the proposed NSFDS technique.  

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References

Chickenpox (Varicella) Overview. http://www.cdc.gov/

Chickenpox (Varicella) Signs & Symptoms. http://www.cdc.gov/

Chickenpox (Varicella) Complications. http://www.cdc.gov/

Routine vaccination against chickenpox? Drug Therapeutics Bull. 2012;50(4):42–45.

Atkinson W. Epidemiology and Prevention of Vaccine-Preventable Diseases, 12th ed. Public Health Foundation. 2011:301–323.

Chickenpox (Varicella) Transmission. http://www.cdc.gov/

Chickenpox (Varicella) Interpreting Laboratory Tests. http://www.cdc.gov/

Oxford University Press (December 2014). "Chickenpox, n."Oed.com. https://www.oed.com/start;jsessionid=72879ACCDAD7A5B6F66BE6BD11C0E3EB?authRejection=true&url=%2Fview%2FEntry%2F31556%3FredirectedFrom%3DChickenpox

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

Fatima U, Ali M, Ahmed N, et al. Numerical modeling of susceptible latent breaking-out quarantine computer virus epidemic dynamics. Heliyon. 2018 May 1;4(5):e00631. https://doi.org/10.1016/j.heliyon.2018.e00631

Ahmed N, Shahid N, Iqbal Z, Jawaz M, Rafiq M, Tahira SS, Ahmad MO. Numerical modeling of SEIQV epidemic model with saturated incidence rate. J Appl Environ Biol Sci. 2018;8(4):67-82.

Riaz MB, Saeed ST, Baleanu D, et al. Computational results with non-singular & non-local kernel flow of viscous fluid in vertical permeable medium with variant temperature. Front Phy. 2020 Sep 4;8:275.

Saeed ST, Khan I, Riaz MB, et al. Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators. J Math. 2020;2020. https://doi.org/10.1155/2020/8890820

Iftikhar N, Saeed ST, Riaz MB. Fractional study on heat and mass transfer of MHD Oldroyd-B fluid with ramped velocity and temperature. Computational Methods for Differential Equations. 2021 Jan 18;126(1):1-21.

Brauer F, Castillo-Chavez C, Castillo-Chavez C. Mathematical models in population biology and epidemiology. New York: Springer; 2012.

Published
2020-12-31
How to Cite
1.
Rafiq M, Ahmed N, Rafique M, Ahmad MO. A Reliable Numerical Analysis of Transmission Dynamics of Chicken Pox (Varicella Zoster Virus). Sci Inquiry Rev. [Internet]. 2020Dec.31 [cited 2024Nov.21];4(4):31-5. Available from: https://journals.umt.edu.pk/index.php/SIR/article/view/1050
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Orignal Article