An Efficient Numerical Method for the Solution of the Polio Virus (Poliomyelitis) Epidemic Model with the Role of Vaccination

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Muhammad Rafique
Naveed Shahid
Nauman Ahmed
Tahira Sumbal Shaikh
Muhammad Asif
Muhammad Ozair Ahmad

Abstract

Mathematical modeling of a communicable disease is an effective way to describe the behavior and dynamics of the disease. It builds on our understanding of the transmission of a contagion in a population. In this paper, we explore the transmission dynamics of the polio virus (poliomyelitis) with vaccination using standard methods. We formulate an unconditionally stable Non-Standard Finite Difference (NSFD) scheme for a continuous system of the epidemic polio virus. The designed scheme to approximate the solution is bounded, consistent with the underlying model. The proposed numerical scheme preserves the positivity of the stated variables which is necessary for any population dynamical system. It is used to calculate the numerical solutions of the epidemic model for different step sizes “h”. Two other numerical schemes are enforced to find the solution of the proposed system. Finally, the comparison of the NSFD technique with these methods proves its validity and effectiveness.

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How to Cite
1.
Rafique M, Shahid N, Ahmed N, Shaikh TS, Asif M, Ahmad MO. An Efficient Numerical Method for the Solution of the Polio Virus (Poliomyelitis) Epidemic Model with the Role of Vaccination. Sci Inquiry Rev. [Internet]. 2020Dec.31 [cited 2021Apr.21];4(4):15-0. Available from: https://journals.umt.edu.pk/index.php/SIR/article/view/1052

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