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Numerical Analysis of Novel Coronavirus (2019-nCov) Pandemic Model with Advection

Shumaila Azam1, Nauman Ahmed1,6, Ali Raza2, Muhammad Sajid Iqbal1, Muhammad Rafiq3, Ilyas Khan4,*, Kottakkaran Sooppy Nisar5, Muhammad Ozair Ahmad1, Zafar Iqbal1,6

1 Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
2 Department of Mathematics, National College of Business Administration and Economics Lahore, Pakistan
3 Faculty of Engineering University of Central Punjab Lahore, Pakistan
4 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, 72915, Vietnam
5 Department of Mathematics, College of Arts and Science at Wadi Aldawaser, Prince Sattam Bin Abdulaziz University, 11991, Alkharj, Kingdom of Saudi Arabia
6 Department of Mathematics, University of Management and Technology, Lahore, Pakistan

* Corresponding Author: Ilyas Khan. Email:

(This article belongs to this Special Issue: Mathematical aspects of the Coronavirus Disease 2019 (COVID-19): Analysis and Control)

Computers, Materials & Continua 2021, 67(3), 2933-2953.


Recently, the world is facing the terror of the novel corona-virus, termed as COVID-19. Various health institutes and researchers are continuously striving to control this pandemic. In this article, the SEIAR (susceptible, exposed, infected, symptomatically infected, asymptomatically infected and recovered) infection model of COVID-19 with a constant rate of advection is studied for the disease propagation. A simple model of the disease is extended to an advection model by accommodating the advection process and some appropriate parameters in the system. The continuous model is transposed into a discrete numerical model by discretizing the domains, finitely. To analyze the disease dynamics, a structure preserving non-standard finite difference scheme is designed. Two steady states of the continuous system are described i.e., virus free steady state and virus existing steady state. Graphical results show that both the steady states of the numerical design coincide with the fixed points of the continuous SEIAR model. Positivity of the state variables is ensured by applying the M-matrix theory. A result for the positivity property is established. For the proposed numerical design, two different types of the stability are investigated. Nonlinear stability and linear stability for the projected scheme is examined by applying some standard results. Von Neuman stability test is applied to ensure linear stability. The reproductive number is described and its pivotal role in stability analysis is also discussed. Consistency and convergence of the numerical model is also studied. Numerical graphs are presented via computer simulations to prove the worth and efficiency of the quarantine factor is explored graphically, which is helpful in controlling the disease dynamics. In the end, the conclusion of the study is also rendered.


Cite This Article

S. Azam, N. Ahmed, A. Raza, M. Sajid Iqbal, M. Rafiq et al., "Numerical analysis of novel coronavirus (2019-ncov) pandemic model with advection," Computers, Materials & Continua, vol. 67, no.3, pp. 2933–2953, 2021.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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