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Computational Modeling of Reaction-Diffusion COVID-19 Model Having Isolated Compartment

Muhammad Shoaib Arif1,2,*, Kamaleldin Abodayeh1, Asad Ejaz2
1 Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
2 Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000, Pakistan
* Corresponding Author: Muhammad Shoaib Arif. Email: marif@psu.edu.sa; shoaib.arif@mail.au.edu.pk
(This article belongs to this Special Issue: Recent Developments on Computational Biology-I)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2022.022235

Received 28 February 2022; Accepted 30 May 2022; Published online 12 July 2022


Cases of COVID-19 and its variant omicron are raised all across the world. The most lethal form and effect of COVID-19 are the omicron version, which has been reported in tens of thousands of cases daily in numerous nations. Following WHO (World health organization) records on 30 December 2021, the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266, active, recovered, and discharge were found to be 82,402 and 34,258,778, respectively. While there were 160,989 active cases, 33,614,434 cured cases, 456,386 total deaths, and 605,885,769 total samples tested. So far, 1,438,322,742 individuals have been vaccinated. The coronavirus or COVID-19 is inciting panic for several reasons. It is a new virus that has affected the whole world. Scientists have introduced certain ways to prevent the virus. One can lower the danger of infection by reducing the contact rate with other persons. Avoiding crowded places and social events with many people reduces the chance of one being exposed to the virus. The deadly COVID-19 spreads speedily. It is thought that the upcoming waves of this pandemic will be even more dreadful. Mathematicians have presented several mathematical models to study the pandemic and predict future dangers. The need of the hour is to restrict the mobility to control the infection from spreading. Moreover, separating affected individuals from healthy people is essential to control the infection. We consider the COVID-19 model in which the population is divided into five compartments. The present model presents the population’s diffusion effects on all susceptible, exposed, infected, isolated, and recovered compartments. The reproductive number, which has a key role in the infectious models, is discussed. The equilibrium points and their stability is presented. For numerical simulations, finite difference (FD) schemes like nonstandard finite difference (NSFD), forward in time central in space (FTCS), and Crank Nicolson (CN) schemes are implemented. Some core characteristics of schemes like stability and consistency are calculated.


Reproductive number; stability; Routh Hurwitz criterion; variational matrix; NSFD scheme; FTCS scheme; Crank Nicolson scheme; consistency
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