Open Access

ARTICLE

Spatio-Temporal Dynamics and Structure Preserving Algorithm for Computer Virus Model

Nauman Ahmed^1,2, Umbreen Fatima¹, Shahzaib Iqbal¹, Ali Raza³, Muhammad Rafiq^4,*, Muhammad Aziz-ur-Rehman², Shehla Saeed¹, Ilyas Khan⁵, Kottakkaran Sooppy Nisar⁶

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, National College of Business Administration and Economics, Lahore, Pakistan
4 Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, Pakistan
5 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh, 72915, Vietnam
6 Department of Mathematics, College of Arts and Sciences at Wadi Aldawaser, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia

* Corresponding Author: Muhammad Rafiq. Email:

Computers, Materials & Continua 2021, 68(1), 201-212. https://doi.org/10.32604/cmc.2021.014171

Received 03 September 2020; Accepted 20 December 2020; Issue published 22 March 2021

Abstract

The present work is related to the numerical investigation of the spatio-temporal susceptible-latent-breaking out-recovered (SLBR) epidemic model. It describes the computer virus dynamics with vertical transmission via the internet. In these types of dynamics models, the absolute values of the state variables are the fundamental requirement that must be fulfilled by the numerical design. By taking into account this key property, the positivity preserving algorithm is designed to solve the underlying SLBR system. Since, the state variables associated with the phenomenon, represent the computer nodes, so they must take in absolute. Moreover, the continuous system (SLBR) acquires two steady states i.e., the virus-free state and the virus existence state. The stability of the numerical design, at the equilibrium points, portrays an exceptional aspect about the propagation of the virus. The designed discretization algorithm sustains the stability of both the steady states. The computer simulations also endorse that the proposed discretization algorithm retains all the traits of the continuous SLBR model with spatial content. The stability and consistency of the proposed algorithm are verified, mathematically. All the facts are also ascertained by numerical simulations.

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Keywords

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