Open Access

ARTICLE

Optimality of Solution with Numerical Investigation for Coronavirus Epidemic Model

Naveed Shahid^1,2, Dumitru Baleanu^3,4,5, Nauman Ahmed^1,2, Tahira Sumbal Shaikh⁶, Ali Raza^7,*, Muhammad Sajid Iqbal¹, Muhammad Rafiq⁸, Muhammad Aziz-ur Rehman²

1 Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
2 Department of Mathematics, University of Management and Technology, Lahore, Pakistan
3 Department of Mathematics, Cankaya University, Balgat, Ankara, 06530, Turkey
4 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
5 Institute of Space Sciences, Magurele-Bucharest, Romania
6 Department of Mathematics, Lahore College for Women University, Lahore, Pakistan
7 Department of Mathematics, National College of Business Administration and Economics Lahore, Pakistan
8 Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, Pakistan

* Corresponding Author: Ali Raza. Email:

Computers, Materials & Continua 2021, 67(2), 1713-1728. https://doi.org/10.32604/cmc.2021.014191

Received 04 September 2020; Accepted 01 December 2020; Issue published 05 February 2021

Abstract

The novel coronavirus disease, coined as COVID-19, is a murderous and infectious disease initiated from Wuhan, China. This killer disease has taken a large number of lives around the world and its dynamics could not be controlled so far. In this article, the spatio-temporal compartmental epidemic model of the novel disease with advection and diffusion process is projected and analyzed. To counteract these types of diseases or restrict their spread, mankind depends upon mathematical modeling and medicine to reduce, alleviate, and anticipate the behavior of disease dynamics. The existence and uniqueness of the solution for the proposed system are investigated. Also, the solution to the considered system is made possible in a well-known functions space. For this purpose, a Banach space of function is chosen and the solutions are optimized in the closed and convex subset of the space. The essential explicit estimates for the solutions are investigated for the associated auxiliary data. The numerical solution and its analysis are the crux of this study. Moreover, the consistency, stability, and positivity are the indispensable and core properties of the compartmental models that a numerical design must possess. To this end, a nonstandard finite difference numerical scheme is developed to find the numerical solutions which preserve the structural properties of the continuous system. The M-matrix theory is applied to prove the positivity of the design. The results for the consistency and stability of the design are also presented in this study. The plausibility of the projected scheme is indicated by an appropriate example. Computer simulations are also exhibited to conclude the results.

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